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2-cyclic permutations of lattice vertex operator algebras


Authors: Chongying Dong, Feng Xu and Nina Yu
Journal: Proc. Amer. Math. Soc. 144 (2016), 3207-3220
MSC (2010): Primary 17B69
DOI: https://doi.org/10.1090/proc/12966
Published electronically: December 21, 2015
MathSciNet review: 3503690
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Abstract | References | Similar Articles | Additional Information

Abstract: The irreducible modules of the 2-cyclic permutation orbifold models of lattice vertex operator algebras of rank one are classified, and the quantum dimensions of irreducible modules and the fusion rules are determined.


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  • [A1] Toshiyuki Abe, Fusion rules for the free bosonic orbifold vertex operator algebra, J. Algebra 229 (2000), no. 1, 333-374. MR 1765784 (2001f:17053), https://doi.org/10.1006/jabr.2000.8311
  • [A2] Toshiyuki Abe, Rationality of the vertex operator algebra $ V_L+$ for a positive definite even lattice $ L$, Math. Z. 249 (2005), no. 2, 455-484. MR 2115454 (2005k:17033), https://doi.org/10.1007/s00209-004-0709-1
  • [A3] Toshiyuki Abe, $ C_2$-cofiniteness of the 2-cycle permutation orbifold models of minimal Virasoro vertex operator algebras, Comm. Math. Phys. 303 (2011), no. 3, 825-844. MR 2786218 (2012d:17047), https://doi.org/10.1007/s00220-011-1209-x
  • [A4] Toshiyuki Abe, $ C_2$-cofiniteness of 2-cyclic permutation orbifold models, Comm. Math. Phys. 317 (2013), no. 2, 425-445. MR 3010190, https://doi.org/10.1007/s00220-012-1618-5
  • [AD] Toshiyuki Abe and Chongying Dong, Classification of irreducible modules for the vertex operator algebra $ V^+_L$: general case, J. Algebra 273 (2004), no. 2, 657-685. MR 2037717 (2005c:17040), https://doi.org/10.1016/j.jalgebra.2003.09.043
  • [ADL] Toshiyuki Abe, Chongying Dong, and Haisheng Li, Fusion rules for the vertex operator algebra $ M(1)$ and $ V^+_L$, Comm. Math. Phys. 253 (2005), no. 1, 171-219. MR 2105641 (2005i:17033), https://doi.org/10.1007/s00220-004-1132-5
  • [Ba] P. Bantay, Characters and modular properties of permutation orbifolds, Phys. Lett. B 419 (1998), no. 1-4, 175-178. MR 1620424 (98m:81165), https://doi.org/10.1016/S0370-2693(97)01464-0
  • [BDM] Katrina Barron, Chongying Dong, and Geoffrey Mason, Twisted sectors for tensor product vertex operator algebras associated to permutation groups, Comm. Math. Phys. 227 (2002), no. 2, 349-384. MR 1903649 (2003f:17034), https://doi.org/10.1007/s002200200633
  • [BHL] Katrina Barron, Yi-Zhi Huang, and James Lepowsky, An equivalence of two constructions of permutation-twisted modules for lattice vertex operator algebras, J. Pure Appl. Algebra 210 (2007), no. 3, 797-826. MR 2324608 (2008f:17043), https://doi.org/10.1016/j.jpaa.2006.12.005
  • [Bo] Richard E. Borcherds, Vertex algebras, Kac-Moody algebras, and the Monster, Proc. Nat. Acad. Sci. U.S.A. 83 (1986), no. 10, 3068-3071. MR 843307 (87m:17033), https://doi.org/10.1073/pnas.83.10.3068
  • [BHS] L. Borisov, M. B. Halpern, and C. Schweigert, Systematic approach to cyclic orbifolds, Internat. J. Modern Phys. A 13 (1998), no. 1, 125-168. MR 1606821 (99i:81068), https://doi.org/10.1142/S0217751X98000044
  • [D1] Chongying Dong, Vertex algebras associated with even lattices, J. Algebra 161 (1993), no. 1, 245-265. MR 1245855 (94j:17023), https://doi.org/10.1006/jabr.1993.1217
  • [D2] Chongying Dong, Twisted modules for vertex algebras associated with even lattices, J. Algebra 165 (1994), no. 1, 91-112. MR 1272580 (95i:17032), https://doi.org/10.1006/jabr.1994.1099
  • [DJL] Chongying Dong, Cuipo Jiang, and Xingjun Lin, Rationality of vertex operator algebra $ V^+_L$: higher rank, Proc. Lond. Math. Soc. (3) 104 (2012), no. 4, 799-826. MR 2908783, https://doi.org/10.1112/plms/pdr055
  • [DJX] Chongying Dong, Xiangyu Jiao, and Feng Xu, Quantum dimensions and quantum Galois theory, Trans. Amer. Math. Soc. 365 (2013), no. 12, 6441-6469. MR 3105758, https://doi.org/10.1090/S0002-9947-2013-05863-1
  • [DL1] Chongying Dong and James Lepowsky, Generalized vertex algebras and relative vertex operators, Progress in Mathematics, vol. 112, Birkhäuser Boston, Inc., Boston, MA, 1993. MR 1233387 (95b:17032)
  • [DL2] Chongying Dong and James Lepowsky, The algebraic structure of relative twisted vertex operators, J. Pure Appl. Algebra 110 (1996), no. 3, 259-295. MR 1393116 (98e:17036), https://doi.org/10.1016/0022-4049(95)00095-X
  • [DLM1] Chongying Dong, Haisheng Li, and Geoffrey Mason, Regularity of rational vertex operator algebras, Adv. Math. 132 (1997), no. 1, 148-166. MR 1488241 (98m:17037), https://doi.org/10.1006/aima.1997.1681
  • [DLM2] Chongying Dong, Haisheng Li, and Geoffrey Mason, Twisted representations of vertex operator algebras, Math. Ann. 310 (1998), no. 3, 571-600. MR 1615132 (99d:17030), https://doi.org/10.1007/s002080050161
  • [DM] Chongying Dong and Geoffrey Mason, On quantum Galois theory, Duke Math. J. 86 (1997), no. 2, 305-321. MR 1430435 (97k:17042), https://doi.org/10.1215/S0012-7094-97-08609-9
  • [DN1] Chongying Dong and Kiyokazu Nagatomo, Classification of irreducible modules for the vertex operator algebra $ M(1)^+$, J. Algebra 216 (1999), no. 1, 384-404. MR 1694542 (2000b:17038), https://doi.org/10.1006/jabr.1998.7784
  • [DN2] Chongying Dong and Kiyokazu Nagatomo, Representations of vertex operator algebra $ V_L^+$ for rank one lattice $ L$, Comm. Math. Phys. 202 (1999), no. 1, 169-195. MR 1686535 (2000b:17037), https://doi.org/10.1007/s002200050578
  • [DN3] Chongying Dong and Kiyokazu Nagatomo, Classification of irreducible modules for the vertex operator algebra $ M(1)^+$. II. Higher rank, J. Algebra 240 (2001), no. 1, 289-325. MR 1830555 (2002e:17037), https://doi.org/10.1006/jabr.2000.8716
  • [DY] Chongying Dong and Gaywalee Yamskulna, Vertex operator algebras, generalized doubles and dual pairs, Math. Z. 241 (2002), no. 2, 397-423. MR 1935493 (2003j:17038), https://doi.org/10.1007/s002090200421
  • [FHL] Igor B. Frenkel, Yi-Zhi Huang, and James Lepowsky, On axiomatic approaches to vertex operator algebras and modules, Mem. Amer. Math. Soc. 104 (1993), no. 494, viii+64. MR 1142494 (94a:17007), https://doi.org/10.1090/memo/0494
  • [FLM] Igor Frenkel, James Lepowsky, and Arne Meurman, Vertex operator algebras and the Monster, Pure and Applied Mathematics, vol. 134, Academic Press, Inc., Boston, MA, 1988. MR 996026 (90h:17026)
  • [Le] J. Lepowsky, Calculus of twisted vertex operators, Proc. Nat. Acad. Sci. U.S.A. 82 (1985), no. 24, 8295-8299. MR 820716 (88f:17030), https://doi.org/10.1073/pnas.82.24.8295
  • [Li] Haisheng Li, Some finiteness properties of regular vertex operator algebras, J. Algebra 212 (1999), no. 2, 495-514. MR 1676852 (2000c:17044), https://doi.org/10.1006/jabr.1998.7654
  • [M] Masahiko Miyamoto, $ C_2$-cofiniteness of cyclic-orbifold models, Comm. Math. Phys. 335 (2015), no. 3, 1279-1286. MR 3320313, https://doi.org/10.1007/s00220-014-2252-1
  • [KLX] Victor G. Kac, Roberto Longo, and Feng Xu, Solitons in affine and permutation orbifolds, Comm. Math. Phys. 253 (2005), no. 3, 723-764. MR 2116735 (2006b:81154), https://doi.org/10.1007/s00220-004-1160-1
  • [Y] Hiroshi Yamauchi, Module categories of simple current extensions of vertex operator algebras, J. Pure Appl. Algebra 189 (2004), no. 1-3, 315-328. MR 2038578 (2005b:17058), https://doi.org/10.1016/j.jpaa.2003.10.006

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Additional Information

Chongying Dong
Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064

Feng Xu
Affiliation: Department of Mathematics, University of California, Riverside, California 92521

Nina Yu
Affiliation: Department of Mathematics, University of California, Riverside, California 92521

DOI: https://doi.org/10.1090/proc/12966
Received by editor(s): July 10, 2015
Received by editor(s) in revised form: September 8, 2015
Published electronically: December 21, 2015
Additional Notes: The first author was supported by NSF grant DMS-1404741, NSA grant H98230-14-1-0118 and China NSF grant 11371261
The second author was partially supported by China NSF 11471064
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2015 American Mathematical Society

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