메뉴 건너뛰기




Volumn 51, Issue 2, 2010, Pages 43-90

Hopf algebras and finite tensor categories in conformal field theory

Author keywords

[No Author keywords available]

Indexed keywords


EID: 79957906158     PISSN: 00416932     EISSN: 16699637     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (30)

References (105)
  • 1
    • 39749185299 scopus 로고    scopus 로고
    • On the triplet vertex algebra W(p)
    • D. Adamovic and A. Milas, On the triplet vertex algebra W(p), Adv.Math. 217 (2008) 2664-2699
    • (2008) Adv. Math. , vol.217 , pp. 2664-2699
    • Adamovic, D.1    Milas, A.2
  • 3
    • 77955811169 scopus 로고    scopus 로고
    • Some remarks on symmetric linear functions and pseudotrace maps
    • Y. Arike, Some remarks on symmetric linear functions and pseudotrace maps, Proc. Japan Acad. Math. Sci. 86 (2010) 119-124.
    • (2010) Proc. Japan Acad. Math. Sci. , vol.86 , pp. 119-124
    • Arike, Y.1
  • 5
    • 77954226429 scopus 로고    scopus 로고
    • On the Rosenberg-Zelinsky sequence in abelian monoidal categories
    • T. Barmeier, J. Fuchs, I. Runkel, and C. Schweigert, On the Rosenberg-Zelinsky sequence in abelian monoidal categories, J. Reine Angew.Math. 642 (2010) 1-36
    • (2010) J. Reine Angew. Math. , vol.642 , pp. 1-36
    • Barmeier, T.1    Fuchs, J.2    Runkel, I.3    Schweigert, C.4
  • 6
    • 77955865820 scopus 로고    scopus 로고
    • Module categories for permutation modular invariants
    • IMRN
    • T. Barmeier, J. Fuchs, I. Runkel, and C. Schweigert, Module categories for permutation modular invariants, Int.Math.Res.Not. IMRN 16 (2010) 3067-3100
    • (2010) Int.Math.Res.Not. , vol.16 , pp. 3067-3100
    • Barmeier, T.1    Fuchs, J.2    Runkel, I.3    Schweigert, C.4
  • 7
    • 0002620325 scopus 로고    scopus 로고
    • Conformal blocks, fusion rules and the Verlinde formula, in: Hirzebruch 65 Conference on Algebraic Geometry
    • M. Teicher, ed. (Bar-Ilan University, Ramat Gan 1996)
    • A. Beauville, Conformal blocks, fusion rules and the Verlinde formula, in: Hirzebruch 65 Conference on Algebraic Geometry [Israel Math.Conf.Proc. 9], M. Teicher, ed. (Bar-Ilan University, Ramat Gan 1996), p. 75-96
    • Israel Math. Conf. Proc. , vol.9 , pp. 75-96
    • Beauville, A.1
  • 8
    • 0347566048 scopus 로고    scopus 로고
    • On the classification of bulk and boundary conformal field theories
    • R.E. Behrend, P.A. Pearce, V.B. Petkova, and J.-B. Zuber, On the classification of bulk and boundary conformal field theories, Phys. Lett. B 444 (1998) 163-166
    • (1998) Phys. Lett. B , vol.444 , pp. 163-166
    • Behrend, R.E.1    Pearce, P.A.2    Petkova, V.B.3    Zuber, J.-B.4
  • 10
    • 24544453124 scopus 로고
    • Boundary conditions, fusion rules and the Verlinde formula
    • J.L. Cardy, Boundary conditions, fusion rules and the Verlinde formula, Nucl.Phys. B 324 (1989) 581-596.
    • (1989) Nucl. Phys. B , vol.324 , pp. 581-596
    • Cardy, J.L.1
  • 11
    • 30644470278 scopus 로고    scopus 로고
    • 2-cofiniteness for a family of W-algebras
    • 2-cofiniteness for a family of W-algebras, J. Phys. A 39 (2006) 951-966
    • (2006) J. Phys. A , vol.39 , pp. 951-966
    • Carqueville, N.1    Flohr, M.2
  • 12
    • 57549103197 scopus 로고    scopus 로고
    • On the relation between the WRT invariant and the Hennings invariant
    • Q. Chen, S. Kuppum, and P. Srinivasan, On the relation between the WRT invariant and the Hennings invariant, Math. Proc. Cambridge Philos. Soc. 146 (2009) 151-163
    • (2009) Math. Proc. Cambridge Philos. Soc. , vol.146 , pp. 151-163
    • Chen, Q.1    Kuppum, S.2    Srinivasan, P.3
  • 13
    • 55649103669 scopus 로고    scopus 로고
    • Characters and a Verlinde-type formula for symmetric Hopf algebras
    • M. Cohen and S. Westreich, Characters and a Verlinde-type formula for symmetric Hopf algebras, J. Algebra 320 (2008) 4300-4316.
    • (2008) J. Algebra , vol.320 , pp. 4300-4316
    • Cohen, M.1    Westreich, S.2
  • 14
    • 79957879204 scopus 로고    scopus 로고
    • A dual version of the ribbon graph decomposition of moduli space
    • K. Costello, A dual version of the ribbon graph decomposition of moduli space, Geom. and Topol. 11 (2007) 1637-1652
    • (2007) Geom. and Topol. , vol.11 , pp. 1637-1652
    • Costello, K.1
  • 16
  • 17
    • 0000405473 scopus 로고
    • A proof for the Verlinde formula
    • G. Faltings, A proof for the Verlinde formula, J. Algebraic Geom. 3 (1994) 347-374.
    • (1994) J. Algebraic Geom. , vol.3 , pp. 347-374
    • Faltings, G.1
  • 18
    • 33646746046 scopus 로고    scopus 로고
    • Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center
    • B.L. Feigin, A.M. Gainutdinov, A.M. Semikhatov, and I.Yu. Tipunin, Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center, Commun.Math. Phys. 265 (2006) 47-93
    • (2006) Commun. Math. Phys. , vol.265 , pp. 47-93
    • Feigin, B.L.1    Gainutdinov, A.M.2    Semikhatov, A.M.3    Tipunin, I.Yu.4
  • 19
    • 33748923994 scopus 로고    scopus 로고
    • Kazhdan-Lusztig correspondence for the representation category of the triplet W-algebra in logarithmic CFT
    • B.L. Feigin, A.M. Gainutdinov, A.M. Semikhatov, and I.Yu. Tipunin, Kazhdan-Lusztig correspondence for the representation category of the triplet W-algebra in logarithmic CFT, Theor.Math. Phys. 148 (2006) 1210-1235
    • (2006) Theor. Math. Phys. , vol.148 , pp. 1210-1235
    • Feigin, B.L.1    Gainutdinov, A.M.2    Semikhatov, A.M.3    Tipunin, I.Yu.4
  • 20
    • 34047164902 scopus 로고    scopus 로고
    • Kazhdan-Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models
    • B.L. Feigin, A.M. Gainutdinov, A.M. Semikhatov, and I.Yu. Tipunin, Kazhdan-Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models, J.Math. Phys. 48 (2007) 032303, 1-46
    • (2007) J. Math. Phys. , vol.48 , pp. 1-46
    • Feigin, B.L.1    Gainutdinov, A.M.2    Semikhatov, A.M.3    Tipunin, I.Yu.4
  • 21
    • 0000455771 scopus 로고    scopus 로고
    • Correlation functions and boundary conditions in RCFT and three-dimensional topology
    • G. Felder, J. Fröhlich, J. Fuchs, and C. Schweigert, Correlation functions and boundary conditions in RCFT and three-dimensional topology, Compos.Math. 131 (2002) 189- 237
    • (2002) Compos. Math. , vol.131 , pp. 189-237
    • Felder, G.1    Fröhlich, J.2    Fuchs, J.3    Schweigert, C.4
  • 22
    • 33750720971 scopus 로고    scopus 로고
    • TFT construction of RCFT correlators V: Proof of modular invariance and factorisation
    • J. Fjelstad, J. Fuchs, I. Runkel, and C. Schweigert, TFT construction of RCFT correlators V: Proof of modular invariance and factorisation, Theory Appl.Categ. 16 (2006) 342-433
    • (2006) Theory Appl. Categ. , vol.16 , pp. 342-433
    • Fjelstad, J.1    Fuchs, J.2    Runkel, I.3    Schweigert, C.4
  • 23
    • 55449124838 scopus 로고    scopus 로고
    • Uniqueness of open/closed rational CFT with given algebra of open states
    • J. Fjelstad, J. Fuchs, I. Runkel, and C. Schweigert, Uniqueness of open/closed rational CFT with given algebra of open states, Adv.Theor.Math. Phys. 12 (2008) 1281-1373
    • (2008) Adv. Theor. Math. Phys. , vol.12 , pp. 1281-1373
    • Fjelstad, J.1    Fuchs, J.2    Runkel, I.3    Schweigert, C.4
  • 24
    • 0346681086 scopus 로고    scopus 로고
    • On fusion rules in logarithmic conformal field theories
    • M. Flohr, On fusion rules in logarithmic conformal field theories, Int. J.Mod.Phys. A 12 (1997) 1943-1958
    • (1997) Int. J. Mod. Phys. A , vol.12 , pp. 1943-1958
    • Flohr, M.1
  • 25
    • 32344434265 scopus 로고    scopus 로고
    • Logarithmic torus amplitudes
    • M. Flohr and M.R. Gaberdiel, Logarithmic torus amplitudes, J. Phys. A 39 (2006) 1955-1967
    • (2006) J. Phys. A , vol.39 , pp. 1955-1967
    • Flohr, M.1    Gaberdiel, M.R.2
  • 27
    • 24444481808 scopus 로고
    • The analytic geometry of two-dimensional conformal field theory
    • D.H. Friedan and S.H. Shenker, The analytic geometry of two-dimensional conformal field theory, Nucl. Phys. B 281 (1987) 509-545.
    • (1987) Nucl. Phys. B , vol.281 , pp. 509-545
    • Friedan, D.H.1    Shenker, S.H.2
  • 29
    • 33846157416 scopus 로고    scopus 로고
    • Duality and defects in rational conformal field theory
    • J. Fr̈ohlich, J. Fuchs, I. Runkel, and C. Schweigert, Duality and defects in rational conformal field theory, Nucl.Phys. B 763 (2007) 354-430
    • (2007) Nucl. Phys. B , vol.763 , pp. 354-430
    • Fr̈ohlich, J.1    Fuchs, J.2    Runkel, I.3    Schweigert, C.4
  • 31
    • 0037060902 scopus 로고    scopus 로고
    • Conformal correlation functions, Frobenius algebras and triangulations
    • J. Fuchs, I. Runkel, and C. Schweigert, Conformal correlation functions, Frobenius algebras and triangulations, Nucl.Phys. B 624 (2002) 452-468
    • (2002) Nucl. Phys. B , vol.624 , pp. 452-468
    • Fuchs, J.1    Runkel, I.2    Schweigert, C.3
  • 32
    • 0037049228 scopus 로고    scopus 로고
    • TFT construction of RCFT correlators I: Partition functions
    • J. Fuchs, I. Runkel, and C. Schweigert, TFT construction of RCFT correlators I: Partition functions, Nucl.Phys. B 646 (2002) 353-497
    • (2002) Nucl. Phys. B , vol.646 , pp. 353-497
    • Fuchs, J.1    Runkel, I.2    Schweigert, C.3
  • 33
    • 0347603901 scopus 로고    scopus 로고
    • TFT construction of RCFT correlators II: Unoriented world sheets
    • J. Fuchs, I. Runkel, and C. Schweigert, TFT construction of RCFT correlators II: Unoriented world sheets, Nucl. Phys. B 678 (2004) 511-637
    • (2004) Nucl. Phys. B , vol.678 , pp. 511-637
    • Fuchs, J.1    Runkel, I.2    Schweigert, C.3
  • 34
    • 4043087990 scopus 로고    scopus 로고
    • TFT construction of RCFT correlators III: Simple currents
    • J. Fuchs, I. Runkel and C. Schweigert, TFT construction of RCFT correlators III: Simple currents, Nucl. Phys. B 694 (2004) 277-353
    • (2004) Nucl. Phys. B , vol.694 , pp. 277-353
    • Fuchs, J.1    Runkel, I.2    Schweigert, C.3
  • 35
    • 17844370264 scopus 로고    scopus 로고
    • TFT construction of RCFT correlators IV: Structure constants and correlation functions
    • J. Fuchs, I. Runkel, and C. Schweigert, TFT construction of RCFT correlators IV: Structure constants and correlation functions, Nucl.Phys. B 715 (2005) 539-638
    • (2005) Nucl. Phys. B , vol.715 , pp. 539-638
    • Fuchs, J.1    Runkel, I.2    Schweigert, C.3
  • 36
    • 40249110303 scopus 로고    scopus 로고
    • Ribbon categories and (unoriented) CFT: Frobenius algebras, automorphisms, reversions
    • J. Fuchs, I. Runkel and C. Schweigert, Ribbon categories and (unoriented) CFT: Frobenius algebras, automorphisms, reversions, Contemp.Math. 431 (2007) 203-224
    • (2007) Contemp. Math. , vol.431 , pp. 203-224
    • Fuchs, J.1    Runkel, I.2    Schweigert, C.3
  • 38
    • 77953254934 scopus 로고    scopus 로고
    • Twenty-five years of two-dimensional rational conformal field theory
    • J. Fuchs, I. Runkel, and C. Schweigert, Twenty-five years of two-dimensional rational conformal field theory, J.Math. Phys. 51 (2010) 015210, 1-19
    • (2010) J. Math. Phys. , vol.51 , pp. 1-19
    • Fuchs, J.1    Runkel, I.2    Schweigert, C.3
  • 39
  • 40
    • 74449093528 scopus 로고    scopus 로고
    • The three-dimensional origin of the classifying algebra
    • J. Fuchs, C. Schweigert, and C. Stigner, The three-dimensional origin of the classifying algebra, Nucl.Phys. B 824 (2010) 333-364
    • (2010) Nucl. Phys. B , vol.824 , pp. 333-364
    • Fuchs, J.1    Schweigert, C.2    Stigner, C.3
  • 41
    • 38949099992 scopus 로고    scopus 로고
    • From boundary to bulk in logarithmic CFT
    • M.R. Gaberdiel and I. Runkel, From boundary to bulk in logarithmic CFT, J. Phys. A41 (2008) 075402, 1-29
    • (2008) J. Phys. , vol.A41 , pp. 1-29
    • Gaberdiel, M.R.1    Runkel, I.2
  • 42
    • 70449584994 scopus 로고    scopus 로고
    • Fusion rules and boundary conditions in the c = 0 triplet model
    • M.R. Gaberdiel, I. Runkel, and S. Wood, Fusion rules and boundary conditions in the c= 0 triplet model, J. Phys. A 42 (2009) 325403, 1-43
    • (2009) J. Phys. A , vol.42 , pp. 1-43
    • Gaberdiel, M.R.1    Runkel, I.2    Wood, S.3
  • 43
    • 70449581137 scopus 로고    scopus 로고
    • Radford, Drinfeld, and Cardy boundary states in (1,P) logarithmic conformal field models
    • A.M. Gainutdinov and I.Yu. Tipunin, Radford, Drinfeld, and Cardy boundary states in (1,P) logarithmic conformal field models, J.Phys. A 42 (2009) 315207 1-29
    • (2009) J. Phys. A , vol.42 , pp. 1-29
    • Gainutdinov, A.M.1    Tipunin, I.Yu.2
  • 44
    • 0037089993 scopus 로고    scopus 로고
    • Boundary conformal field theory and fusion ring representations
    • T. Gannon, Boundary conformal field theory and fusion ring representations, Nucl. Phys. B 627 (2002) 506-564
    • (2002) Nucl. Phys. B , vol.627 , pp. 506-564
    • Gannon, T.1
  • 45
    • 23844459840 scopus 로고    scopus 로고
    • Modular data: the algebraic combinatorics of conformal field theory
    • T. Gannon, Modular data: the algebraic combinatorics of conformal field theory, J. Algebraic Combin. 22 (2005) 211-250
    • (2005) J. Algebraic Combin. , vol.22 , pp. 211-250
    • Gannon, T.1
  • 46
    • 0001274392 scopus 로고    scopus 로고
    • Invariants of links and 3-manifolds obtained from Hopf algebras
    • M.A. Hennings, Invariants of links and 3-manifolds obtained from Hopf algebras, J. London Math. Soc. 54 (1996) 594-624.
    • (1996) J. London Math. Soc. , vol.54 , pp. 594-624
    • Hennings, M.A.1
  • 47
    • 17244380729 scopus 로고    scopus 로고
    • Vertex operator algebras, the Verlinde conjecture and modular tensor categories
    • Y.-Z. Huang, Vertex operator algebras, the Verlinde conjecture and modular tensor categories, Proc.Natl.Acad. Sci.USA 102 (2005) 5352-5356
    • (2005) Proc. Natl. Acad. Sci. USA , vol.102 , pp. 5352-5356
    • Huang, Y.-Z.1
  • 48
    • 33846176355 scopus 로고    scopus 로고
    • Vertex operator algebras, fusion rules and modular transformations
    • Y.-Z. Huang, Vertex operator algebras, fusion rules and modular transformations, Contemp. Math. 391 (2005) 135-148
    • (2005) Contemp. Math. , vol.391 , pp. 135-148
    • Huang, Y.-Z.1
  • 49
    • 58149513975 scopus 로고    scopus 로고
    • Cofiniteness conditions, projective covers and the logarithmic tensor product theory
    • Y.-Z. Huang, Cofiniteness conditions, projective covers and the logarithmic tensor product theory, J. Pure Appl.Algebra 213 (2009) 458-475
    • (2009) J. Pure Appl. Algebra , vol.213 , pp. 458-475
    • Huang, Y.-Z.1
  • 50
    • 79957884792 scopus 로고    scopus 로고
    • Representations of vertex operator algebras and braided finite tensor categories
    • Y.-Z. Huang, Representations of vertex operator algebras and braided finite tensor categories, Contemp.Math. 497 (2009) 97-111
    • (2009) Contemp. Math. , vol.497 , pp. 97-111
    • Huang, Y.-Z.1
  • 52
    • 0001645660 scopus 로고
    • A theory of tensor products for module categories for a vertex operator algebra, III
    • Y.-Z. Huang and J. Lepowsky, A theory of tensor products for module categories for a vertex operator algebra, III, J. Pure Appl.Algebra 100 (1995) 141-171
    • (1995) J. Pure Appl. Algebra , vol.100 , pp. 141-171
    • Huang, Y.-Z.1    Lepowsky, J.2
  • 54
  • 55
    • 0032378672 scopus 로고    scopus 로고
    • Modular repreyentations of simple Lie algebras
    • J.E. Humphreys, Modular repreyentations of simple Lie algebras, Bull.Amer.Math. Soc. 35 (1998) 105-122.
    • (1998) Bull. Amer. Math. Soc. , vol.35 , pp. 105-122
    • Humphreys, J.E.1
  • 56
    • 44949283969 scopus 로고
    • The geometry of tensor calculus, I
    • A. Joyal and R. Street, The geometry of tensor calculus, I, Adv.Math. 88 (1991) 55-112.
    • (1991) Adv. Math. , vol.88 , pp. 55-112
    • Joyal, A.1    Street, R.2
  • 57
    • 0006731313 scopus 로고    scopus 로고
    • Separability and Hopf algebras
    • L. Kadison and A.A. Stolin, Separability and Hopf algebras, Contemp.Math. 259 (2000) 279-296.
    • (2000) Contemp. Math. , vol.259 , pp. 279-296
    • Kadison, L.1    Stolin, A.A.2
  • 58
    • 0003704279 scopus 로고
    • (Springer Verlag, New York)
    • C. Kassel, Quantum Groups (Springer Verlag, New York 1995).
    • (1995) Quantum Groups
    • Kassel, C.1
  • 59
    • 0000909641 scopus 로고
    • Invariants of 3-manifolds derived from finite dimensional Hopf algebras
    • L.H. Kauffman and D.E. Radford, Invariants of 3-manifolds derived from finite dimensional Hopf algebras, J. Knot Theory Ramifications 4 (1995) 131-162
    • (1995) J. Knot Theory Ramifications , vol.4 , pp. 131-162
    • Kauffman, L.H.1    Radford, D.E.2
  • 60
    • 0001400413 scopus 로고
    • Extended conformal algebras generated by a multiplet of primary fields
    • H. Kausch, Extended conformal algebras generated by a multiplet of primary fields, Phys. Lett. B 259 (1991) 448-455.
    • (1991) Phys. Lett. B , vol.259 , pp. 448-455
    • Kausch, H.1
  • 61
    • 0035373595 scopus 로고    scopus 로고
    • Multi-interval subfactors and modularity of representations in conformal field theory
    • Y. Kawahigashi, R. Longo, and M. Müger, Multi-interval subfactors and modularity of representations in conformal field theory, Commun.Math.Phys. 219 (2001) 631-669
    • (2001) Commun. Math. Phys. , vol.219 , pp. 631-669
    • Kawahigashi, Y.1    Longo, R.2    Müger, M.3
  • 62
    • 0039131275 scopus 로고
    • Mapping class group actions on quantum doubles
    • T. Kerler, Mapping class group actions on quantum doubles, Commun.Math. Phys. 168 (1995) 353-388
    • (1995) Commun. Math. Phys. , vol.168 , pp. 353-388
    • Kerler, T.1
  • 65
    • 0037058440 scopus 로고    scopus 로고
    • On q-analog of the McKay correspondence and the ADE classification of sl(2) conformal field theories
    • A.A. Kirillov and V. Ostrik, On q-analog of the McKay correspondence and the ADE classification of sl(2) conformal field theories, Adv.Math. 171 (2002) 183-227
    • (2002) Adv. Math. , vol.171 , pp. 183-227
    • Kirillov, A.A.1    Ostrik, V.2
  • 67
    • 49249139373 scopus 로고    scopus 로고
    • Cardy condition for open-closed field algebras
    • L. Kong, Cardy condition for open-closed field algebras, Commun.Math. Phys. 283 (2008) 25-92
    • (2008) Commun. Math. Phys. , vol.283 , pp. 25-92
    • Kong, L.1
  • 68
    • 70350604588 scopus 로고    scopus 로고
    • Cardy algebras and sewing constraints, I
    • L. Kong and I. Runkel, Cardy algebras and sewing constraints, I, Commun.Math. Phys. 292 (2009) 871-912
    • (2009) Commun. Math. Phys. , vol.292 , pp. 871-912
    • Kong, L.1    Runkel, I.2
  • 71
    • 79957883225 scopus 로고    scopus 로고
    • On the classification of topological field theories
    • J. Lurie, On the classification of topological field theories, Current Developments in Mathematics 2008 (2009) 129-280
    • (2009) Current Developments in Mathematics , vol.2008 , pp. 129-280
    • Lurie, J.1
  • 72
    • 21844485595 scopus 로고
    • Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity
    • V.V. Lyubashenko, Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity, Commun.Math. Phys. 172 (1995) 467-516
    • (1995) Commun. Math. Phys. , vol.172 , pp. 467-516
    • Lyubashenko, V.V.1
  • 73
    • 33748919033 scopus 로고
    • Modular transformations for tensor categories
    • V.V. Lyubashenko, Modular transformations for tensor categories, J. Pure Appl. Algebra 98 (1995) 279-327.
    • (1995) J. Pure Appl. Algebra , vol.98 , pp. 279-327
    • Lyubashenko, V.V.1
  • 74
    • 0000977747 scopus 로고
    • Braided groups and quantum Fourier transform
    • V.V. Lyubashenko and S. Majid, Braided groups and quantum Fourier transform, J. Algebra 166 (1994) 506-528.
    • (1994) J. Algebra , vol.166 , pp. 506-528
    • Lyubashenko, V.V.1    Majid, S.2
  • 77
    • 2142696493 scopus 로고    scopus 로고
    • 2-cofiniteness
    • 2-cofiniteness, Duke Math. J. 122 (2004) 51-91
    • (2004) Duke Math. J , vol.122 , pp. 51-91
    • Miyamoto, M.1
  • 79
    • 0346763470 scopus 로고
    • Classical and quantum conformal field theory
    • G. Moore and N. Seiberg, Classical and quantum conformal field theory, Commun. Math. Phys. 123 (1989) 177-254.
    • (1989) Commun. Math. Phys. , vol.123 , pp. 177-254
    • Moore, G.1    Seiberg, N.2
  • 80
    • 55849134827 scopus 로고    scopus 로고
    • Logarithmic knot invariants arising from restricted quantum groups
    • J. Murakami and K. Nagatomo, Logarithmic knot invariants arising from restricted quantum groups, Int. J.Math. 19 (2008) 1203-1213
    • (2008) Int. J. Math , vol.19 , pp. 1203-1213
    • Murakami, J.1    Nagatomo, K.2
  • 82
    • 30444434707 scopus 로고    scopus 로고
    • Frobenius-Schur indicators for a class of fusion categories
    • S. Natale, Frobenius-Schur indicators for a class of fusion categories, Pacific J.Math. 221 (2005) 353-377
    • (2005) Pacific J. Math. , vol.221 , pp. 353-377
    • Natale, S.1
  • 83
    • 33847106814 scopus 로고    scopus 로고
    • Frobenius-Schur indicators and exponents of spherical categories
    • S.-H. Ng and P. Schauenburg, Frobenius-Schur indicators and exponents of spherical categories, Adv.Math. 211 (2007) 34-71.
    • (2007) Adv. Math. , vol.211 , pp. 34-71
    • Ng, S.-H.1    Schauenburg, P.2
  • 84
    • 0038012493 scopus 로고    scopus 로고
    • Quantum groupoids and invariants of knots and 3-manifolds
    • D. Nikshych, V. Turaev, and L. Vainerman, Quantum groupoids and invariants of knots and 3-manifolds, Topology Appl. 127 (2003) 91-123
    • (2003) Topology Appl , vol.127 , pp. 91-123
    • Nikshych, D.1    Turaev, V.2    Vainerman, L.3
  • 85
    • 0038309312 scopus 로고    scopus 로고
    • Module categories, weak Hopf algebras and modular invariants
    • V. Ostrik, Module categories, weak Hopf algebras and modular invariants, Transform. Groups 8 (2003) 177-206
    • (2003) Transform. Groups , vol.8 , pp. 177-206
    • Ostrik, V.1
  • 86
    • 0000230174 scopus 로고
    • When Hopf algebras are Frobenius algebras
    • B. Pareigis, When Hopf algebras are Frobenius algebras, J. Algebra 18 (1971) 588-596.
    • (1971) J. Algebra , vol.18 , pp. 588-596
    • Pareigis, B.1
  • 87
    • 52349111947 scopus 로고    scopus 로고
    • Integrable boundary conditions and Wextended fusion in the logarithmic minimal models L?(1???)
    • P.A. Pearce, J. Rasmussen, and P. Ruelle, Integrable boundary conditions and Wextended fusion in the logarithmic minimal models L?(1???), J.Phys. A 41 (2008) 295201, 1-16
    • (2008) J. Phys. A , vol.41 , pp. 1-16
    • Pearce, P.A.1    Rasmussen, J.2    Ruelle, P.3
  • 88
    • 84888595413 scopus 로고    scopus 로고
    • Grothendieck ring and Verlinde formula for the W-extended logarithmic minimal model λM(1, p)
    • P.A. Pearce, J. Rasmussen, and P. Ruelle, Grothendieck ring and Verlinde formula for the W-extended logarithmic minimal model λM(1, p), J.Phys. A 43 (2010) 045211, 1-13
    • (2010) J. Phys. A , vol.43 , pp. 1-13
    • Pearce, P.A.1    Rasmussen, J.2    Ruelle, P.3
  • 89
    • 84921773489 scopus 로고    scopus 로고
    • Fusion of irreducible modules in WLM(1, p)
    • J. Rasmussen, Fusion of irreducible modules in WLM(1, p), J.Phys. A 43 (2010) 045210, 1-27
    • (2010) J. Phys. A , vol.43 , pp. 1-27
    • Rasmussen, J.1
  • 91
    • 0542373499 scopus 로고
    • Invariants of 3-manifolds via link polynomials and quantum groups
    • N.Yu. Reshetikhin and V.G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent.math. 103 (1991) 547-597.
    • (1991) Invent. math. , vol.103 , pp. 547-597
    • Reshetikhin, N.Y.1    Turaev, V.G.2
  • 93
    • 0001694570 scopus 로고
    • Simple currents, modular invariants, and fixed points
    • A.N. Schellekens and S. Yankielowicz, Simple currents, modular invariants, and fixed points, Int. J.Mod.Phys. A 5 (1990) 2903-2952.
    • (1990) Int. J. Mod. Phys. A , vol.5 , pp. 2903-2952
    • Schellekens, A.N.1    Yankielowicz, S.2
  • 95
    • 84878103405 scopus 로고    scopus 로고
    • Categorification and correlation functions in conformal field theory
    • M. Sanz-Solé, J. Soria, J. L. Varona, and J. Verdera, eds. (European Mathematical Society, Zürich 2006)
    • C. Schweigert, J. Fuchs, and I. Runkel, Categorification and correlation functions in conformal field theory, in: Proceedings of the ICM 2006, M. Sanz-Soĺe, J. Soria, J.L. Varona, and J. Verdera, eds. (European Mathematical Society, Z̈urich 2006), p. 443- 458
    • (2006) in: Proceedings of the ICM , pp. 443-458
    • Schweigert, C.1    Fuchs, J.2    Runkel, I.3
  • 96
    • 41049090961 scopus 로고    scopus 로고
    • Factorizable ribbon quantum groups in logarithmic conformal field theories
    • A.M. Semikhatov, Factorizable ribbon quantum groups in logarithmic conformal field theories, Theor.Math. Phys. 154 (2008) 433-453
    • (2008) Theor. Math. Phys. , vol.154 , pp. 433-453
    • Semikhatov, A.M.1
  • 97
    • 0003179687 scopus 로고    scopus 로고
    • La formule de Verlinde
    • Ch. Sorger, La formule de Verlinde, Astérisque 237 (1996) 87-114
    • (1996) Astérisque , vol.237 , pp. 87-114
    • Sorger, Ch.1
  • 99
    • 0000333180 scopus 로고
    • Conformal field theory on universal family of stable curves with gauge symmetries
    • A. Tsuchiya, K. Ueno, and H. Yamada, Conformal field theory on universal family of stable curves with gauge symmetries, Adv. Studies in Pure Math. 19 (1989) 459-566.
    • (1989) Adv. Studies in Pure Math. , vol.19 , pp. 459-566
    • Tsuchiya, A.1    Ueno, K.2    Yamada, H.3
  • 101
    • 45549111952 scopus 로고
    • Fusion rules and modular transformations in 2D conformal field theory
    • E. Verlinde, Fusion rules and modular transformations in 2D conformal field theory, Nucl.Phys. B 300 (1988) 360-376.
    • (1988) Nucl. Phys. B , vol.300 , pp. 360-376
    • Verlinde, E.1
  • 102
    • 33746862524 scopus 로고    scopus 로고
    • Kirby elements and quantum invariants
    • A. Virelizier, Kirby elements and quantum invariants, Proc. London Math. Soc. 93 (2006) 474-514
    • (2006) Proc. London Math. Soc. , vol.93 , pp. 474-514
    • Virelizier, A.1
  • 103
    • 14644388676 scopus 로고
    • Quantum field theory and the Jones polynomial
    • E. Witten, Quantum field theory and the Jones polynomial, Commun.Math. Phys. 121 (1989) 351-399.
    • (1989) Commun. Math. Phys. , vol.121 , pp. 351-399
    • Witten, E.1
  • 104
    • 75849131199 scopus 로고    scopus 로고
    • p,q triplet models
    • p,q triplet models, J. Phys. A 43 (2010) 045212, 1-18
    • (2010) J. Phys. A , vol.43 , pp. 1-18
    • Wood, S.1
  • 105
    • 0039269198 scopus 로고    scopus 로고
    • t(sl(2)) at root of unity
    • t(sl(2)) at root of unity, Canad. J. Math. 49 (1997) 772-787.
    • (1997) Canad. J. Math. , vol.49 , pp. 772-787
    • Xiao, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.