2-cyclic permutations of lattice vertex operator algebras
HTML articles powered by AMS MathViewer
- by Chongying Dong, Feng Xu and Nina Yu PDF
- Proc. Amer. Math. Soc. 144 (2016), 3207-3220 Request permission
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.References
- Toshiyuki Abe, Fusion rules for the free bosonic orbifold vertex operator algebra, J. Algebra 229 (2000), no.ย 1, 333โ374. MR 1765784, DOI 10.1006/jabr.2000.8311
- Toshiyuki Abe, Rationality of the vertex operator algebra $V_L+$ for a positive definite even lattice $L$, Math. Z. 249 (2005), no.ย 2, 455โ484. MR 2115454, DOI 10.1007/s00209-004-0709-1
- Toshiyuki Abe, $C_2$-cofiniteness of the 2-cycle permutation orbifold models of minimal Virasoro vertex operator algebras, Comm. Math. Phys. 303 (2011), no.ย 3, 825โ844. MR 2786218, DOI 10.1007/s00220-011-1209-x
- Toshiyuki Abe, $C_2$-cofiniteness of 2-cyclic permutation orbifold models, Comm. Math. Phys. 317 (2013), no.ย 2, 425โ445. MR 3010190, DOI 10.1007/s00220-012-1618-5
- Toshiyuki Abe and Chongying Dong, Classification of irreducible modules for the vertex operator algebra $V^+_L$: general case, J. Algebra 273 (2004), no.ย 2, 657โ685. MR 2037717, DOI 10.1016/j.jalgebra.2003.09.043
- 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.ย 1, 171โ219. MR 2105641, DOI 10.1007/s00220-004-1132-5
- P. Bantay, Characters and modular properties of permutation orbifolds, Phys. Lett. B 419 (1998), no.ย 1-4, 175โ178. MR 1620424, DOI 10.1016/S0370-2693(97)01464-0
- 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.ย 2, 349โ384. MR 1903649, DOI 10.1007/s002200200633
- 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.ย 3, 797โ826. MR 2324608, DOI 10.1016/j.jpaa.2006.12.005
- Richard E. Borcherds, Vertex algebras, Kac-Moody algebras, and the Monster, Proc. Nat. Acad. Sci. U.S.A. 83 (1986), no.ย 10, 3068โ3071. MR 843307, DOI 10.1073/pnas.83.10.3068
- L. Borisov, M. B. Halpern, and C. Schweigert, Systematic approach to cyclic orbifolds, Internat. J. Modern Phys. A 13 (1998), no.ย 1, 125โ168. MR 1606821, DOI 10.1142/S0217751X98000044
- Chongying Dong, Vertex algebras associated with even lattices, J. Algebra 161 (1993), no.ย 1, 245โ265. MR 1245855, DOI 10.1006/jabr.1993.1217
- Chongying Dong, Twisted modules for vertex algebras associated with even lattices, J. Algebra 165 (1994), no.ย 1, 91โ112. MR 1272580, DOI 10.1006/jabr.1994.1099
- Chongying Dong, Cuipo Jiang, and Xingjun Lin, Rationality of vertex operator algebra $V^+_L$: higher rank, Proc. Lond. Math. Soc. (3) 104 (2012), no.ย 4, 799โ826. MR 2908783, DOI 10.1112/plms/pdr055
- Chongying Dong, Xiangyu Jiao, and Feng Xu, Quantum dimensions and quantum Galois theory, Trans. Amer. Math. Soc. 365 (2013), no.ย 12, 6441โ6469. MR 3105758, DOI 10.1090/S0002-9947-2013-05863-1
- Chongying Dong and James Lepowsky, Generalized vertex algebras and relative vertex operators, Progress in Mathematics, vol. 112, Birkhรคuser Boston, Inc., Boston, MA, 1993. MR 1233387, DOI 10.1007/978-1-4612-0353-7
- Chongying Dong and James Lepowsky, The algebraic structure of relative twisted vertex operators, J. Pure Appl. Algebra 110 (1996), no.ย 3, 259โ295. MR 1393116, DOI 10.1016/0022-4049(95)00095-X
- Chongying Dong, Haisheng Li, and Geoffrey Mason, Regularity of rational vertex operator algebras, Adv. Math. 132 (1997), no.ย 1, 148โ166. MR 1488241, DOI 10.1006/aima.1997.1681
- Chongying Dong, Haisheng Li, and Geoffrey Mason, Twisted representations of vertex operator algebras, Math. Ann. 310 (1998), no.ย 3, 571โ600. MR 1615132, DOI 10.1007/s002080050161
- Chongying Dong and Geoffrey Mason, On quantum Galois theory, Duke Math. J. 86 (1997), no.ย 2, 305โ321. MR 1430435, DOI 10.1215/S0012-7094-97-08609-9
- Chongying Dong and Kiyokazu Nagatomo, Classification of irreducible modules for the vertex operator algebra $M(1)^+$, J. Algebra 216 (1999), no.ย 1, 384โ404. MR 1694542, DOI 10.1006/jabr.1998.7784
- Chongying Dong and Kiyokazu Nagatomo, Representations of vertex operator algebra $V_L^+$ for rank one lattice $L$, Comm. Math. Phys. 202 (1999), no.ย 1, 169โ195. MR 1686535, DOI 10.1007/s002200050578
- Chongying Dong and Kiyokazu Nagatomo, Classification of irreducible modules for the vertex operator algebra $M(1)^+$. II. Higher rank, J. Algebra 240 (2001), no.ย 1, 289โ325. MR 1830555, DOI 10.1006/jabr.2000.8716
- Chongying Dong and Gaywalee Yamskulna, Vertex operator algebras, generalized doubles and dual pairs, Math. Z. 241 (2002), no.ย 2, 397โ423. MR 1935493, DOI 10.1007/s002090200421
- 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.ย 494, viii+64. MR 1142494, DOI 10.1090/memo/0494
- 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
- J. Lepowsky, Calculus of twisted vertex operators, Proc. Nat. Acad. Sci. U.S.A. 82 (1985), no.ย 24, 8295โ8299. MR 820716, DOI 10.1073/pnas.82.24.8295
- Haisheng Li, Some finiteness properties of regular vertex operator algebras, J. Algebra 212 (1999), no.ย 2, 495โ514. MR 1676852, DOI 10.1006/jabr.1998.7654
- Masahiko Miyamoto, $C_2$-cofiniteness of cyclic-orbifold models, Comm. Math. Phys. 335 (2015), no.ย 3, 1279โ1286. MR 3320313, DOI 10.1007/s00220-014-2252-1
- Victor G. Kac, Roberto Longo, and Feng Xu, Solitons in affine and permutation orbifolds, Comm. Math. Phys. 253 (2005), no.ย 3, 723โ764. MR 2116735, DOI 10.1007/s00220-004-1160-1
- Hiroshi Yamauchi, Module categories of simple current extensions of vertex operator algebras, J. Pure Appl. Algebra 189 (2004), no.ย 1-3, 315โ328. MR 2038578, DOI 10.1016/j.jpaa.2003.10.006
Additional Information
- Chongying Dong
- Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064
- MR Author ID: 316207
- Feng Xu
- Affiliation: Department of Mathematics, University of California, Riverside, California 92521
- MR Author ID: 358033
- Nina Yu
- Affiliation: Department of Mathematics, University of California, Riverside, California 92521
- MR Author ID: 830351
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3207-3220
- MSC (2010): Primary 17B69
- DOI: https://doi.org/10.1090/proc/12966
- MathSciNet review: 3503690