메뉴 건너뛰기




Volumn 10, Issue SUPPL. 1, 2008, Pages 1049-1074

On exotic modular tensor categories

Author keywords

Drinfeld center; Modular category; Quantum group; Topological quantum field theory

Indexed keywords


EID: 56749158634     PISSN: 02191997     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219199708003162     Document Type: Article
Times cited : (38)

References (61)
  • 1
    • 0033478706 scopus 로고    scopus 로고
    • Exotic subfactors of finite depth with Jones indices (5 + V13)/2 and (5 + y17)/2
    • M. Asaeda, U. Haagerup, Exotic subfactors of finite depth with Jones indices (5 + V13)/2 and (5 + y17)/2, Comm. Math. Phys. 202 (1999) 1-63.
    • (1999) Comm. Math. Phys , vol.202 , pp. 1-63
    • Asaeda, M.1    Haagerup, U.2
  • 2
    • 0037328183 scopus 로고    scopus 로고
    • The kernel of the modular representation and the Galois action in RCFT
    • P. Bantay, The kernel of the modular representation and the Galois action in RCFT, Comm. Math. Phys. 233 (2003) 423-438.
    • (2003) Comm. Math. Phys , vol.233 , pp. 423-438
    • Bantay, P.1
  • 3
    • 0001501540 scopus 로고
    • A classification of subgroup truncations of the bosonic string
    • F. Bais, P. Bouwknegt, A classification of subgroup truncations of the bosonic string, Nucl. Phys. B 279 (1987) 561-570.
    • (1987) Nucl. Phys. B , vol.279 , pp. 561-570
    • Bais, F.1    Bouwknegt, P.2
  • 5
    • 0013406573 scopus 로고    scopus 로고
    • Lectures on Tensor Categories and Modular Functors
    • Amer. Math. Soc
    • B. Bakalov, A. Kirillov, Jr., Lectures on Tensor Categories and Modular Functors, University Lecture Series, vol. 21 (Amer. Math. Soc., 2001).
    • (2001) University Lecture Series , vol.21
    • Bakalov, B.1    Kirillov Jr., A.2
  • 9
    • 0000680015 scopus 로고
    • Topological gauge theories and group cohomology
    • R. Dijkgraaf, E. Witten, Topological gauge theories and group cohomology, Comm. Math. Phys. 129 (1990) 393-429.
    • (1990) Comm. Math. Phys , vol.129 , pp. 393-429
    • Dijkgraaf, R.1    Witten, E.2
  • 11
    • 0032219320 scopus 로고    scopus 로고
    • Some properties of finite dimensional semisimple Hopf algebras
    • P. Etingof, S. Gelaki, Some properties of finite dimensional semisimple Hopf algebras, Math. Res. Lett. 5 (1998) 191-197.
    • (1998) Math. Res. Lett , vol.5 , pp. 191-197
    • Etingof, P.1    Gelaki, S.2
  • 13
    • 33846831566 scopus 로고    scopus 로고
    • Modular invariants and their fusion rules
    • Contemp. Math, Amer. Math. Soc, Providence, RI
    • D. Evans, P. Pinto, Modular invariants and their fusion rules, in Advances in quantum dynamics (South Hadley, MA, 2002), Contemp. Math., Vol. 335 (Amer. Math. Soc., Providence, RI, 2003), pp. 119-130.
    • (2003) Advances in quantum dynamics (South Hadley, MA, 2002) , vol.335 , pp. 119-130
    • Evans, D.1    Pinto, P.2
  • 14
    • 56749122840 scopus 로고    scopus 로고
    • Modular invariants and the double of the Haagerup subfactor
    • Advances in operator algebras and mathematical physics, Theta, Bucharest
    • D. Evans, P. Pinto, Modular invariants and the double of the Haagerup subfactor, Advances in operator algebras and mathematical physics, Theta Ser. Adv. Math., Vol. 5 (Theta, Bucharest, 2005), pp. 67-88.
    • (2005) Theta Ser. Adv. Math , vol.5 , pp. 67-88
    • Evans, D.1    Pinto, P.2
  • 16
    • 56749113089 scopus 로고    scopus 로고
    • W. Feit, On finite linear groups in dimension at most 10, in Proceedings of the Conference on Finite Groups (Univ. Utah, Park City, Utah, 1975) (Academic Press, New York, 1976), pp. 397-407.
    • W. Feit, On finite linear groups in dimension at most 10, in Proceedings of the Conference on Finite Groups (Univ. Utah, Park City, Utah, 1975) (Academic Press, New York, 1976), pp. 397-407.
  • 18
    • 0030304011 scopus 로고    scopus 로고
    • An equivalence of fusion categories
    • M. Finkelberg, An equivalence of fusion categories, Geom. Funct. Anal. 6 (1996) 249-267
    • (1996) Geom. Funct. Anal , vol.6 , pp. 249-267
    • Finkelberg, M.1
  • 19
    • 21344477849 scopus 로고
    • Chern-Simons theory with finite gauge group
    • D. Freed, F. Quinn, Chern-Simons theory with finite gauge group, Comm. Math. Phys. 156 (1993) 435-472.
    • (1993) Comm. Math. Phys , vol.156 , pp. 435-472
    • Freed, D.1    Quinn, F.2
  • 20
    • 56749134985 scopus 로고    scopus 로고
    • The GAP Group, GAP, Groups, Algorithms, and Programming, Version 4.4.10, 2007
    • The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.4.10, 2007, (http://www.gap-system.org)
  • 22
    • 56749136938 scopus 로고    scopus 로고
    • T. Hagge, S. Hong, Some non-braided fusion categories of rank 3, arXiv: 0704.0208
    • T. Hagge, S. Hong, Some non-braided fusion categories of rank 3, arXiv: 0704.0208
  • 23
    • 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
  • 24
    • 56749175748 scopus 로고    scopus 로고
    • Rigidity and modularity of vertex tensor categories
    • Y.-Z. Huang, Rigidity and modularity of vertex tensor categories, Comm. Contemp. Math. 10 (2008) 871-911.
    • (2008) Comm. Contemp. Math , vol.10 , pp. 871-911
    • Huang, Y.-Z.1
  • 25
    • 0035626715 scopus 로고    scopus 로고
    • The structure of sectors associated with Longo-Rehren inclusions. II. Examples
    • M. Izumi, The structure of sectors associated with Longo-Rehren inclusions. II. Examples, Rev. Math. Phys. 13 (2001) 603-674.
    • (2001) Rev. Math. Phys , vol.13 , pp. 603-674
    • Izumi, M.1
  • 26
    • 0010806038 scopus 로고
    • index for subfactors
    • V. Jones, index for subfactors, Invent. Math. 72 (1983) 1-25.
    • (1983) Invent. Math , vol.72 , pp. 1-25
    • Jones, V.1
  • 27
    • 0003356644 scopus 로고
    • Quantum Groups
    • Springer-Verlag, New York
    • C. Kassel, Quantum Groups, Graduate Texts in Mathematics, Vol. 155 (Springer-Verlag, New York, 1995).
    • (1995) Graduate Texts in Mathematics , vol.155
    • Kassel, C.1
  • 28
    • 0037268624 scopus 로고    scopus 로고
    • Fault-tolerant quantum computation by anyons
    • A. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Physics 303 (2003) 2-30.
    • (2003) Ann. Physics , vol.303 , pp. 2-30
    • Kitaev, A.1
  • 29
    • 30444456387 scopus 로고    scopus 로고
    • Anyons in an exactly solved model and beyond
    • A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Physics 321 (2006) 2-111.
    • (2006) Ann. Physics , vol.321 , pp. 2-111
    • Kitaev, A.1
  • 30
    • 15944387050 scopus 로고    scopus 로고
    • Classification of local conformai nets: Case c 1
    • Y. Kawahigashi, R. Longo, Classification of local conformai nets: Case c 1, Ann. Math. 160 (2004) 493-522.
    • (2004) Ann. Math , vol.160 , pp. 493-522
    • Kawahigashi, Y.1    Longo, R.2
  • 31
    • 0035373595 scopus 로고    scopus 로고
    • Multi-interval subfactors and modularity of representations in conformai field theory
    • Y. Kawahigashi, R. Longo, M. Müger, Multi-interval subfactors and modularity of representations in conformai field theory, Comm. Math. Phys. 219 (2001) 613-669.
    • (2001) Comm. Math. Phys , vol.219 , pp. 613-669
    • Kawahigashi, Y.1    Longo, R.2    Müger, M.3
  • 32
    • 33746926394 scopus 로고    scopus 로고
    • The N-eigenvalue problem and two applications
    • M. J. Larsen, E. C. R.owell, Z. Wang, The N-eigenvalue problem and two applications, Int. Math. R.es. Not. 2005 (2005) 3987-4018.
    • (2005) Int. Math. R.es. Not , vol.2005 , pp. 3987-4018
    • Larsen, M.J.1    owell, E.C.R.2    Wang, Z.3
  • 33
    • 0032345272 scopus 로고    scopus 로고
    • Abelian Chern-Simons theory. I. A topological quantum field theory
    • M. Manoliu, Abelian Chern-Simons theory. I. A topological quantum field theory, J. Math. Phys. 39 (1998) 170-206.
    • (1998) J. Math. Phys , vol.39 , pp. 170-206
    • Manoliu, M.1
  • 34
    • 0037400855 scopus 로고    scopus 로고
    • From subfactor to categories and topology, II
    • M. Müger, From subfactor to categories and topology, II, J. Pure Appl. Algebra 180 (2003) 159-219.
    • (2003) J. Pure Appl. Algebra , vol.180 , pp. 159-219
    • Müger, M.1
  • 35
    • 0242642938 scopus 로고    scopus 로고
    • On the structure of modular categories
    • M. Müger, On the structure of modular categories, Proc. London Math. Soc. 87 (2003) 291-308.
    • (2003) Proc. London Math. Soc , vol.87 , pp. 291-308
    • Müger, M.1
  • 36
    • 18844416449 scopus 로고    scopus 로고
    • Conformai orbifold theories and braided crossed G-categories
    • M. M̈ger, Conformai orbifold theories and braided crossed G-categories, Comm. Math. Phys. 260 (2005) 727-762.
    • (2005) Comm. Math. Phys , vol.260 , pp. 727-762
    • M̈ger, M.1
  • 38
    • 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
  • 40
    • 0346763470 scopus 로고
    • Classical and quantum conformai field theory
    • G. Moore, N. Seiberg, Classical and quantum conformai field theory, Comm. Math. Phys. 123 (1989) 177-254.
    • (1989) Comm. Math. Phys , vol.123 , pp. 177-254
    • Moore, G.1    Seiberg, N.2
  • 41
    • 0002286501 scopus 로고
    • Braid group statistics and their superselection rules
    • World Sci. Publ, River Edge, NJ
    • K. -H. Rehren, Braid group statistics and their superselection rules, The algebraic theory of superselection sectors (Palermo, 1989) (World Sci. Publ., River Edge, NJ, 1990), pp. 333-355.
    • (1990) The algebraic theory of superselection sectors (Palermo, 1989) , pp. 333-355
    • Rehren, K.-H.1
  • 42
    • 41949114993 scopus 로고    scopus 로고
    • From quantum groups to unitary modular tensor categories
    • E. C. Rowell, From quantum groups to unitary modular tensor categories, Contemp. Math. 413 (2006) 215-230.
    • (2006) Contemp. Math , vol.413 , pp. 215-230
    • Rowell, E.C.1
  • 43
    • 23744461408 scopus 로고    scopus 로고
    • E. C. R.owell, On a family of non-unitarizable ribbon categories, Math. Z. 250 (2005) 745-774.
    • E. C. R.owell, On a family of non-unitarizable ribbon categories, Math. Z. 250 (2005) 745-774.
  • 44
    • 41949141454 scopus 로고    scopus 로고
    • Unitarizablity of premodular categories
    • E. C. Rowell, Unitarizablity of premodular categories, J. Pure Appl. Alg. 212 (2008) 1878-1887.
    • (2008) J. Pure Appl. Alg , vol.212 , pp. 1878-1887
    • Rowell, E.C.1
  • 45
    • 56749099123 scopus 로고    scopus 로고
    • E. Rowell, R. Stong, Z. Wang, On classification of modular tensor categories, math.QA/0712.1377.
    • E. Rowell, R. Stong, Z. Wang, On classification of modular tensor categories, math.QA/0712.1377.
  • 46
    • 0542373499 scopus 로고
    • Invariants of 3-manifolds via link polynomials and quantum groups
    • N. Reshetikhin, V. 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.1    Turaev, V.2
  • 47
    • 21144478637 scopus 로고
    • Meromorphic c = 24 conformai field theories
    • A. N. Schellekens, Meromorphic c = 24 conformai field theories, Comm. Math. Phys 153 (1993) 159-185.
    • (1993) Comm. Math. Phys , vol.153 , pp. 159-185
    • Schellekens, A.N.1
  • 48
    • 0001066562 scopus 로고
    • Presentations of the groups SL(2, m) and PSL(2, m)
    • J. Sunday, Presentations of the groups SL(2, m) and PSL(2, m), Canad. J. Math. 24 (1972) 1129-1131.
    • (1972) Canad. J. Math , vol.24 , pp. 1129-1131
    • Sunday, J.1
  • 51
    • 44049114062 scopus 로고
    • State sum invariants of 3-manifolds and quantum 6 j-symbols
    • V. Turaev and O. Viro, State sum invariants of 3-manifolds and quantum 6 j-symbols, Topology 31 (1992) 865-902.
    • (1992) Topology , vol.31 , pp. 865-902
    • Turaev, V.1    Viro, O.2
  • 52
    • 21644488503 scopus 로고    scopus 로고
    • On braided tensor categories of type
    • I. Tuba, H. Wenzl, On braided tensor categories of type BCD J. reine angew. Math, 581 (2005) 31-69.
    • (2005) BCD J. reine angew. Math , vol.581 , pp. 31-69
    • Tuba, I.1    Wenzl, H.2
  • 53
    • 33846810116 scopus 로고    scopus 로고
    • Mirror extensions of local nets
    • F. Xu, Mirror extensions of local nets, Comm. Math. Phys. 270 (2007) 835-847.
    • (2007) Comm. Math. Phys , vol.270 , pp. 835-847
    • Xu, F.1
  • 54
    • 14644390296 scopus 로고    scopus 로고
    • 3-manifold invariants from cosets
    • F. Xu, 3-manifold invariants from cosets, J. Knot Theory Ramifications 14 (2005) 21-90.
    • (2005) J. Knot Theory Ramifications , vol.14 , pp. 21-90
    • Xu, F.1
  • 55
    • 33748560533 scopus 로고    scopus 로고
    • Some computations in the cyclic permutations of completely rational nets
    • F. Xu, Some computations in the cyclic permutations of completely rational nets, Comm. Math. Phys. 267 (2006) 757-782.
    • (2006) Comm. Math. Phys , vol.267 , pp. 757-782
    • Xu, F.1
  • 56
    • 56749088634 scopus 로고    scopus 로고
    • Topologization of electron liquids with Chern-Simons theory and quantum computation
    • Differential geometry and physics, World Sci. Publ, Hackensack, NJ
    • Z. Wang, Topologization of electron liquids with Chern-Simons theory and quantum computation, Differential geometry and physics, Nankai Tracts Math., Vol. 10 (World Sci. Publ., Hackensack, NJ, 2006), 106-120.
    • (2006) Nankai Tracts Math , vol.10 , pp. 106-120
    • Wang, Z.1
  • 57
    • 0032396086 scopus 로고    scopus 로고
    • C* tensor categories from quantum groups
    • H. Wenzl, C* tensor categories from quantum groups, J. Amar. Math. Soc. 11 (1998) 261-282.
    • (1998) J. Amar. Math. Soc , vol.11 , pp. 261-282
    • Wenzl, H.1
  • 59
    • 14644388676 scopus 로고
    • Quantum field theory and the Jones polynomial
    • E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351-399.
    • (1989) Comm. Math. Phys , vol.121 , pp. 351-399
    • Witten, E.1
  • 60
    • 0009258914 scopus 로고
    • The central charge in three dimensions
    • World Sci. Publ, Teaneck, NJ
    • E. Witten, The central charge in three dimensions, Physics and mathematics of strings (World Sci. Publ., Teaneck, NJ, 1990), pp. 530-559.
    • (1990) Physics and mathematics of strings , pp. 530-559
    • Witten, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.