메뉴 건너뛰기




Volumn 10, Issue SUPPL. 1, 2008, Pages 871-911

Rigidity and modularity of vertex tensor categories

Author keywords

Modular tensor category; Modules; Rigidity; Vertex operator algebras

Indexed keywords


EID: 56749175748     PISSN: 02191997     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219199708003083     Document Type: Article
Times cited : (252)

References (47)
  • 2
    • 56749122867 scopus 로고    scopus 로고
    • T. Abe and K. Nagatomo, Finiteness of conformai blocks over the projective line, in: Vertex operator algebras in mathematics and physics (Toronto, 2000), ed. S. Berman, Y. Billig, Y.-Z. Huang and J. Lepowsky, Fields Inst. Commun., 39, Amer. Math. Soc., Providence, 2003, 1-12.
    • T. Abe and K. Nagatomo, Finiteness of conformai blocks over the projective line, in: Vertex operator algebras in mathematics and physics (Toronto, 2000), ed. S. Berman, Y. Billig, Y.-Z. Huang and J. Lepowsky, Fields Inst. Commun., Vol. 39, Amer. Math. Soc., Providence, 2003, 1-12.
  • 3
    • 0000618828 scopus 로고
    • Rationality in conformai field theory
    • G. Anderson and G. Moore, Rationality in conformai field theory, Comm. Math. Phys. 117 (1988) 441-450.
    • (1988) Comm. Math. Phys , vol.117 , pp. 441-450
    • Anderson, G.1    Moore, G.2
  • 4
    • 56749088665 scopus 로고    scopus 로고
    • B. Bakalov and A. Kirillov, Jr., Lectures on tensor categories and modular functors, University Lecture Series, 21, Amer. Math. Soc., Providence, RI, 2001.
    • B. Bakalov and A. Kirillov, Jr., Lectures on tensor categories and modular functors, University Lecture Series, Vol. 21, Amer. Math. Soc., Providence, RI, 2001.
  • 5
    • 0010882054 scopus 로고
    • Infinite conformai symmetries in two-dimensional quantum field theory
    • A. A. Belavin, A. M. Polyakov and A. B. Zamolodchikov, Infinite conformai symmetries in two-dimensional quantum field theory, Nucl. Phys. B241 (1984) 333-380.
    • (1984) Nucl. Phys , vol.B241 , pp. 333-380
    • Belavin, A.A.1    Polyakov, A.M.2    Zamolodchikov, A.B.3
  • 6
    • 0001056693 scopus 로고
    • Vertex algebras, Kac-Moody algebras, and the Monster
    • R.. E. Borcherds, Vertex algebras, Kac-Moody algebras, and the Monster, Proc. Natl. Acad. Sci. USA 83 (1986) 3068-3071.
    • (1986) Proc. Natl. Acad. Sci. USA , vol.83 , pp. 3068-3071
    • Borcherds, R.E.1
  • 9
    • 0034288951 scopus 로고    scopus 로고
    • Modular-invariance of trace functions in orbifold theory and generalized Moonshine
    • C. Dong, H. Li and G. Mason, Modular-invariance of trace functions in orbifold theory and generalized Moonshine, Comm. Math. Phys. 214 (2000) 1-56.
    • (2000) Comm. Math. Phys , vol.214 , pp. 1-56
    • Dong, C.1    Li, H.2    Mason, G.3
  • 11
    • 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
  • 12
    • 0002668119 scopus 로고
    • On axiomatic approaches to vertex operator algebras and modules, preprint, 1989
    • I. B. Frenkel, Y.-Z. Huang and J. Lepowsky, On axiomatic approaches to vertex operator algebras and modules, preprint, 1989; Memoirs Amer. Math. Soc. 104 1993.
    • (1993) Memoirs Amer. Math. Soc , vol.104
    • Frenkel, I.B.1    Huang, Y.-Z.2    Lepowsky, J.3
  • 13
    • 0001761027 scopus 로고
    • A natural representation of the Fischer-Griess Monster with the modular function J as character
    • I. B. Frenkel, J. Lepowsky and A. Meurman, A natural representation of the Fischer-Griess Monster with the modular function J as character, Proc. Natl. Acad. Sci. USA 81 (1984) 3256-3260.
    • (1984) Proc. Natl. Acad. Sci. USA , vol.81 , pp. 3256-3260
    • Frenkel, I.B.1    Lepowsky, J.2    Meurman, A.3
  • 15
    • 0037660883 scopus 로고    scopus 로고
    • Rationality, quasirationality and finite W-algebras
    • M. R. Gaberdiel and A. Neitzke, Rationality, quasirationality and finite W-algebras, Comm. Math. Phys. 238 (2003) 305-331.
    • (2003) Comm. Math. Phys , vol.238 , pp. 305-331
    • Gaberdiel, M.R.1    Neitzke, A.2
  • 16
    • 0001645655 scopus 로고
    • A theory of tensor products for module categories for a, vertex operator algebra, IV
    • Y.-Z. Huang, A theory of tensor products for module categories for a, vertex operator algebra, IV, J. Pure Appl. Alg. 100 (1995) 173-216.
    • (1995) J. Pure Appl. Alg , vol.100 , pp. 173-216
    • Huang, Y.-Z.1
  • 17
    • 0030585266 scopus 로고    scopus 로고
    • Virasoro vertex operator algebras, (nonmeromorphic) operator product expansion and the tensor product theory
    • Y.-Z. Huang, Virasoro vertex operator algebras, (nonmeromorphic) operator product expansion and the tensor product theory, J. Alg. 182 (1996) 201-234.
    • (1996) J. Alg , vol.182 , pp. 201-234
    • Huang, Y.-Z.1
  • 18
    • 56749147046 scopus 로고    scopus 로고
    • Y.-Z. Huang, Intertwining operator algebras, genus-zero modular functors and genus-zero conformai field theories, in: Operads: Proceedings of Renaissance Conferences, ed. J.-L. Loday, J. Stasheff, and A. A. Voronov, Contemporary Math., 202, Amer. Math. Soc., Providence, 1997, 335-355.
    • Y.-Z. Huang, Intertwining operator algebras, genus-zero modular functors and genus-zero conformai field theories, in: Operads: Proceedings of Renaissance Conferences, ed. J.-L. Loday, J. Stasheff, and A. A. Voronov, Contemporary Math., Vol. 202, Amer. Math. Soc., Providence, 1997, 335-355.
  • 19
    • 0001010565 scopus 로고    scopus 로고
    • Generalized rationality and a "Jacobi identity" for intertwining operator algebras
    • Y.-Z. Huang, Generalized rationality and a "Jacobi identity" for intertwining operator algebras, Selecta Math. (N. S.), 6 (2000), 225-267.
    • (2000) Selecta Math. (N. S.) , vol.6 , pp. 225-267
    • Huang, Y.-Z.1
  • 20
    • 20644454895 scopus 로고    scopus 로고
    • Differential equations and intertwining operators
    • Y.-Z. Huang, Differential equations and intertwining operators, Comm. Contemp. Math. 7 (2005), 375-400.
    • (2005) Comm. Contemp. Math , vol.7 , pp. 375-400
    • Huang, Y.-Z.1
  • 21
    • 26444584940 scopus 로고    scopus 로고
    • Differential equations, duality and modular invariance
    • Y.-Z. Huang, Differential equations, duality and modular invariance, Comm. Con-temp. Math.7 (2005) 649-706.
    • (2005) Comm. Con-temp. Math , vol.7 , pp. 649-706
    • Huang, Y.-Z.1
  • 22
    • 18944406392 scopus 로고    scopus 로고
    • Vertex operator algebras and the Verlinde conjecture
    • to appear; math.QA/0406291
    • Y.-Z. Huang, Vertex operator algebras and the Verlinde conjecture, to appear; math.QA/0406291.
    • Huang, Y.-Z.1
  • 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
    • 33846176355 scopus 로고    scopus 로고
    • Vertex operator algebras, fusion rules and modular transformations
    • Non-commutative Geometry and Representation Theory in Mathematical Physics, ed. J. Fuchs, J. Mickelsson, G. Rozenblioum and A. Stolin, Amer. Math. Soc, Providence
    • Y.-Z. Huang, Vertex operator algebras, fusion rules and modular transformations, in: Non-commutative Geometry and Representation Theory in Mathematical Physics, ed. J. Fuchs, J. Mickelsson, G. Rozenblioum and A. Stolin, Contemporary Math. Vol. 391, Amer. Math. Soc., Providence, 2005, 135-148.
    • (2005) Contemporary Math , vol.391 , pp. 135-148
    • Huang, Y.-Z.1
  • 25
    • 0000893321 scopus 로고
    • A theory of tensor products for module categories for a vertex operator algebra, I
    • Y.-Z. Huang and J. Lepowsky, A theory of tensor products for module categories for a vertex operator algebra, I, Selecta Math. (N.S.) 1 (1995) 699-756.
    • (1995) Selecta Math. (N.S.) , vol.1 , pp. 699-756
    • Huang, Y.-Z.1    Lepowsky, J.2
  • 26
    • 34249759387 scopus 로고
    • A theory of tensor products for module categories for a vertex operator algebra, II
    • Y.-Z. Huang and J. Lepowsky, A theory of tensor products for module categories for a vertex operator algebra, II, Selecta Math. (N.S.) 1 (1995) 757-786.
    • (1995) Selecta Math. (N.S.) , vol.1 , pp. 757-786
    • Huang, Y.-Z.1    Lepowsky, J.2
  • 27
    • 0002624352 scopus 로고
    • Tensor products of modules for a vertex operator-algebra and vertex tensor categories
    • ed. R. Brylinski, J.-L. Brylinski, V. Guillemin, V. Kac, Birkhäuser, Boston
    • Y.-Z. Huang and J. Lepowsky, Tensor products of modules for a vertex operator-algebra and vertex tensor categories, in: Lie Theory and Geometry, in honor of Bertram Kostant, ed. R. Brylinski, J.-L. Brylinski, V. Guillemin, V. Kac, Birkhäuser, Boston, 1994, 349-383.
    • (1994) Lie Theory and Geometry, in honor of Bertram Kostant , pp. 349-383
    • Huang, Y.-Z.1    Lepowsky, J.2
  • 28
    • 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. Alg. 100 (1995) 141-171.
    • (1995) J. Pure Appl. Alg , vol.100 , pp. 141-171
    • Huang, Y.-Z.1    Lepowsky, J.2
  • 29
    • 0000713264 scopus 로고    scopus 로고
    • Intertwining operator algebras and vertex tensor categories for affine Lie algebras
    • Y.-Z. Huang and J. Lepowsky, Intertwining operator algebras and vertex tensor categories for affine Lie algebras, Duke Math. J. 99 (1999) 113-134.
    • (1999) Duke Math. J , vol.99 , pp. 113-134
    • Huang, Y.-Z.1    Lepowsky, J.2
  • 30
    • 0004340935 scopus 로고    scopus 로고
    • A theory of tensor products for module categories for a vertex operator algebra, V
    • to appear
    • Y.-Z. Huang and J. Lepowsky, A theory of tensor products for module categories for a vertex operator algebra, V, to appear.
    • Huang, Y.-Z.1    Lepowsky, J.2
  • 31
    • 33749176664 scopus 로고    scopus 로고
    • A logarithmic generalization of tensor product theory for modules for a vertex operator algebra
    • Y.-Z. Huang, J. Lepowsky and L. Zhang, A logarithmic generalization of tensor product theory for modules for a vertex operator algebra, Internat. J. Math. 17 (2006) 975-1012.
    • (2006) Internat. J. Math , vol.17 , pp. 975-1012
    • Huang, Y.-Z.1    Lepowsky, J.2    Zhang, L.3
  • 33
    • 84960598757 scopus 로고    scopus 로고
    • D. Kazhdan and G. Lusztig, Affine Lie algebras and quantum groups, International Mathematics Research Notices (in Duke Math. J.) 2 (1991) 21-29.
    • D. Kazhdan and G. Lusztig, Affine Lie algebras and quantum groups, International Mathematics Research Notices (in Duke Math. J.) 2 (1991) 21-29.
  • 34
    • 84968466254 scopus 로고
    • Tensor structures arising from affine Lie algebras, I
    • D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras, I, J. Amar. Math. Soc. 6 (1993) 905-947.
    • (1993) J. Amar. Math. Soc , vol.6 , pp. 905-947
    • Kazhdan, D.1    Lusztig, G.2
  • 35
    • 84968502641 scopus 로고
    • Tensor structures arising from affine Lie algebras, II
    • D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras, II, J. Amar. Math. Soc. 6 (1993) 949-1011.
    • (1993) J. Amar. Math. Soc , vol.6 , pp. 949-1011
    • Kazhdan, D.1    Lusztig, G.2
  • 36
    • 84968516064 scopus 로고
    • Tensor structures arising from affine Lie algebras, III
    • D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras, III, J. Amar. Math. Soc. 7 (1994) 335-381.
    • (1994) J. Amar. Math. Soc , vol.7 , pp. 335-381
    • Kazhdan, D.1    Lusztig, G.2
  • 37
    • 84968469508 scopus 로고
    • Tensor structures arising from affine Lie algebras, IV
    • D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras, IV, J. Amar. Math. Soc. 7 (1994) 383-453.
    • (1994) J. Amar. Math. Soc , vol.7 , pp. 383-453
    • Kazhdan, D.1    Lusztig, G.2
  • 38
    • 17244380958 scopus 로고    scopus 로고
    • Prom the representation theory of vertex operator algebras to modular tensor categories in conformai field theory
    • J. Lepowsky, Prom the representation theory of vertex operator algebras to modular tensor categories in conformai field theory, Proc. Natl. Acad. Sci. USA 102 (2005) 5304-5305.
    • (2005) Proc. Natl. Acad. Sci. USA , vol.102 , pp. 5304-5305
    • Lepowsky, J.1
  • 39
    • 0033556813 scopus 로고    scopus 로고
    • Some finiteness properties of regular vertex operator algebras
    • H. Li, Some finiteness properties of regular vertex operator algebras, J. Alg. 212 (1999) 495-514.
    • (1999) J. Alg , vol.212 , pp. 495-514
    • Li, H.1
  • 40
    • 56749141599 scopus 로고    scopus 로고
    • M. Miyamoto, Intertwining operators and modular invariance, to appear; math. QA/0010180.
    • M. Miyamoto, Intertwining operators and modular invariance, to appear; math. QA/0010180.
  • 41
    • 0010798477 scopus 로고
    • Polynomial equations for rational conformai field theories
    • G. Moore and N. Seiberg, Polynomial equations for rational conformai field theories, Phys. Lett. B 212 (1988) 451-460.
    • (1988) Phys. Lett. B , vol.212 , pp. 451-460
    • Moore, G.1    Seiberg, N.2
  • 42
    • 0346763470 scopus 로고
    • Classical and quantum conformai field theory
    • G. Moore and 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
  • 44
    • 45549111952 scopus 로고
    • Fusion rules and modular transformations in 2D conformai field theory
    • E. Verlinde, Fusion rules and modular transformations in 2D conformai field theory, Nucl. Phys. B300 (1988) 360-376.
    • (1988) Nucl. Phys , vol.B300 , pp. 360-376
    • Verlinde, E.1
  • 47
    • 0030551014 scopus 로고    scopus 로고
    • Modular invariance of characters of vertex operator algebras
    • Y. Zhu, Modular invariance of characters of vertex operator algebras, J. Amer. Math. Soc. 9 (1996) 237-307.
    • (1996) J. Amer. Math. Soc , vol.9 , pp. 237-307
    • Zhu, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.