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Mirror extensions of rational vertex operator algebras.(English)Zbl 1433.17036

From the introduction: In this paper, mirror extensions of rational vertex operator algebras are considered. The mirror extension conjecture is proved.
Mirror extensions were first studied in the context of conformal nets; new conformalnets were obtained, and it was further proved that these conformal nets cannot be obtained by cosets, orbifolds and simple current extensions [Feng Xu, Commun. Math. Phys. 270, No. 3, 835–847 (2007;Zbl 1121.81111). ]. The mirrorextensions of vertex operator algebras were studied in [C. Dong et al., Commun. Math. Phys. 329, No. 1, 263–294 (2014;Zbl 1295.81086)]: mirror extensions ofspecific vertex operator algebras were obtained, and it was conjectured that the mirrorextensions exist for general vertex operator algebras satisfying some conditions. …
It was conjectured in [Dong et al., loc. cit.] that if there is a vertex operator algebra structure on \(V^e\) such that \(V^e\) is an extension vertex operator algebra of \(V\), then \((V^c)^e\) has a vertex operator algebra structure such that \((V^c)^e\) is an extension vertex operator algebra of \(V^c\), the so-called mirror extension vertex operator algebra of \(V^c\). The main goal of this paper is to prove this conjecture.

MSC:

17B69 Vertex operators; vertex operator algebras and related structures

Cite

References:

[1]Abe, Toshiyuki; Buhl, Geoffrey; Dong, Chongying, Rationality, regularity, and \(C_2\)-cofiniteness, Trans. Amer. Math. Soc., 356, 8, 3391-3402 (electronic) (2004) ·Zbl 1070.17011 ·doi:10.1090/S0002-9947-03-03413-5
[2]Abe, Toshiyuki; Dong, Chongying; Li, Haisheng, Fusion rules for the vertex operator algebra \(M(1)\) and \(V^+_L\), Comm. Math. Phys., 253, 1, 171-219 (2005) ·Zbl 1207.17032 ·doi:10.1007/s00220-004-1132-5
[3]Bakalov, Bojko; Kirillov, Alexander, Jr., Lectures on tensor categories and modular functors, University Lecture Series 21, x+221 pp. (2001), American Mathematical Society, Providence, RI ·Zbl 0965.18002
[4]Davydov, Alexei; M{\"u}ger, Michael; Nikshych, Dmitri; Ostrik, Victor, The Witt group of non-degenerate braided fusion categories, J. Reine Angew. Math., 677, 135-177 (2013) ·Zbl 1271.18008
[5]Dong, Chongying; Jiao, Xiangyu; Xu, Feng, Mirror extensions of vertex operator algebras, Comm. Math. Phys., 329, 1, 263-294 (2014) ·Zbl 1295.81086 ·doi:10.1007/s00220-014-1933-0
[6]Dong, Chongying; Jiao, Xiangyu; Xu, Feng, Quantum dimensions and quantum Galois theory, Trans. Amer. Math. Soc., 365, 12, 6441-6469 (2013) ·Zbl 1337.17018 ·doi:10.1090/S0002-9947-2013-05863-1
[7]Dong, Chongying; Li, Haisheng; Mason, Geoffrey, Regularity of rational vertex operator algebras, Adv. Math., 132, 1, 148-166 (1997) ·Zbl 0902.17014 ·doi:10.1006/aima.1997.1681
[8]Dong, Chongying; Mason, Geoffrey; Zhu, Yongchang, Discrete series of the Virasoro algebra and the moonshine module. Algebraic groups and their generalizations: quantum and infinite-dimensional methods, University Park, PA, 1991, Proc. Sympos. Pure Math. 56, 295-316 (1994), Amer. Math. Soc., Providence, RI ·Zbl 0813.17019
[9]Etingof, Pavel; Nikshych, Dmitri; Ostrik, Viktor, On fusion categories, Ann. of Math. (2), 162, 2, 581-642 (2005) ·Zbl 1125.16025 ·doi:10.4007/annals.2005.162.581
[10]Frenkel, I. B., Representations of affine Lie algebras, Hecke modular forms and Korteweg-de Vries type equations. Lie algebras and related topics, New Brunswick, N.J., 1981, Lecture Notes in Math. 933, 71-110 (1982), Springer, Berlin-New York ·Zbl 0505.17008
[11]Frenkel, Igor B.; Huang, Yi-Zhi; Lepowsky, James, On axiomatic approaches to vertex operator algebras and modules, Mem. Amer. Math. Soc., 104, 494, viii+64 pp. (1993) ·Zbl 0789.17022 ·doi:10.1090/memo/0494
[12]Frenkel, Igor; Lepowsky, James; Meurman, Arne, Vertex operator algebras and the Monster, Pure and Applied Mathematics 134, liv+508 pp. (1988), Academic Press, Inc., Boston, MA ·Zbl 0674.17001
[13]Frenkel, Igor B.; Zhu, Yongchang, Vertex operator algebras associated to representations of affine and Virasoro algebras, Duke Math. J., 66, 1, 123-168 (1992) ·Zbl 0848.17032 ·doi:10.1215/S0012-7094-92-06604-X
[14]Huang, Yi-Zhi, A theory of tensor products for module categories for a vertex operator algebra. IV, J. Pure Appl. Algebra, 100, 1-3, 173-216 (1995) ·Zbl 0841.17015 ·doi:10.1016/0022-4049(95)00050-7
[15]Huang, Yi-Zhi, Virasoro vertex operator algebras, the (nonmeromorphic) operator product expansion and the tensor product theory, J. Algebra, 182, 1, 201-234 (1996) ·Zbl 0862.17022 ·doi:10.1006/jabr.1996.0168
[16]Huang, Yi-Zhi, Differential equations and intertwining operators, Commun. Contemp. Math., 7, 3, 375-400 (2005) ·Zbl 1070.17012 ·doi:10.1142/S0219199705001799
[17]Huang, Yi-Zhi, Rigidity and modularity of vertex tensor categories, Commun. Contemp. Math., 10, suppl. 1, 871-911 (2008) ·Zbl 1169.17019 ·doi:10.1142/S0219199708003083
[18]Huang, Yi-Zhi; Kirillov, Alexander, Jr.; Lepowsky, James, Braided tensor categories and extensions of vertex operator algebras, Comm. Math. Phys., 337, 3, 1143-1159 (2015) ·Zbl 1388.17014 ·doi:10.1007/s00220-015-2292-1
[19]Huang, Y.-Z.; Lepowsky, J., A theory of tensor products for module categories for a vertex operator algebra. I, Selecta Math. (N.S.), 1, 4, 699-756 (1995) ·Zbl 0854.17032 ·doi:10.1007/BF01587908
[20]Huang, Y.-Z.; Lepowsky, J., A theory of tensor products for module categories for a vertex operator algebra. II, Selecta Math. (N.S.), 1, 4, 757-786 (1995) ·Zbl 0854.17032 ·doi:10.1007/BF01587908
[21]Huang, Yi-Zhi; Lepowsky, James, A theory of tensor products for module categories for a vertex operator algebra. III, J. Pure Appl. Algebra, 100, 1-3, 141-171 (1995) ·Zbl 0841.17014 ·doi:10.1016/0022-4049(95)00049-3
[22]Huang, Yi-Zhi; Lepowsky, James, Tensor products of modules for a vertex operator algebra and vertex tensor categories. Lie theory and geometry, Progr. Math. 123, 349-383 (1994), Birkh\"auser Boston, Boston, MA ·Zbl 0848.17031
[23]Kassel, Christian, Quantum groups, Graduate Texts in Mathematics 155, xii+531 pp. (1995), Springer-Verlag, New York ·Zbl 0808.17003 ·doi:10.1007/978-1-4612-0783-2
[24]Kirillov, Alexander, Jr.; Ostrik, Viktor, On a \(q\)-analogue of the McKay correspondence and the ADE classification of \(\mathfrak{sl}_2\) conformal field theories, Adv. Math., 171, 2, 183-227 (2002) ·Zbl 1024.17013 ·doi:10.1006/aima.2002.2072
[25]Lepowsky, James; Li, Haisheng, Introduction to vertex operator algebras and their representations, Progress in Mathematics 227, xiv+318 pp. (2004), Birkh\"auser Boston, Inc., Boston, MA ·Zbl 1055.17001 ·doi:10.1007/978-0-8176-8186-9
[26]Li, Haisheng, Some finiteness properties of regular vertex operator algebras, J. Algebra, 212, 2, 495-514 (1999) ·Zbl 0953.17017 ·doi:10.1006/jabr.1998.7654
[27]M{\"u}ger, Michael, On the structure of modular categories, Proc. London Math. Soc. (3), 87, 2, 291-308 (2003) ·Zbl 1037.18005 ·doi:10.1112/S0024611503014187
[28]M{\"u}ger, Michael, From subfactors to categories and topology. II. The quantum double of tensor categories and subfactors, J. Pure Appl. Algebra, 180, 1-2, 159-219 (2003) ·Zbl 1033.18003 ·doi:10.1016/S0022-4049(02)00248-7
[29]Nakanishi, Tomoki; Tsuchiya, Akihiro, Level-rank duality of WZW models in conformal field theory, Comm. Math. Phys., 144, 2, 351-372 (1992) ·Zbl 0751.17024
[30]Ostrik, Victor, Module categories, weak Hopf algebras and modular invariants, Transform. Groups, 8, 2, 177-206 (2003) ·Zbl 1044.18004 ·doi:10.1007/s00031-003-0515-6
[31]Ostrik, Victor; Sun, Michael, Level-rank duality via tensor categories, Comm. Math. Phys., 326, 1, 49-61 (2014) ·Zbl 1371.18006 ·doi:10.1007/s00220-013-1869-9
[32]Xu, Feng, Mirror extensions of local nets, Comm. Math. Phys., 270, 3, 835-847 (2007) ·Zbl 1121.81111 ·doi:10.1007/s00220-006-0184-0
[33]Zhu, Yongchang, Modular invariance of characters of vertex operator algebras, J. Amer. Math. Soc., 9, 1, 237-302 (1996) ·Zbl 0854.17034 ·doi:10.1090/S0894-0347-96-00182-8
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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