Frontiers of Mathematics in China >
Constructing tensor products of modules for C2-cofinite vertex operator superalgebras
Received date: 01 Mar 2014
Accepted date: 13 Mar 2014
Published date: 24 Jun 2014
Copyright
For any C2-cofinite vertex operator superalgebra V, the tensor product and the P(z)-tensor product of any two admissible V-modules of finite length are proved to exist, which are shown to be isomorphic, and their constructions are given explicitly in this paper.
Key words: vertex operator superalgebra; tensor product; C2-cofiniteness
Jianzhi HAN . Constructing tensor products of modules for C2-cofinite vertex operator superalgebras[J]. Frontiers of Mathematics in China, 2014 , 9(3) : 477 -494 . DOI: 10.1007/s11464-014-0369-3
1 |
AbeT, BuhlG, DongC Y. Rationality, regularity, and C2-cofiniteness. Trans Amer Math Soc, 2004, 356: 3391-3402
|
2 |
BuhlG. A spanning set for VOA modules. J Algebra, 2002, 254: 125-151
|
3 |
BuhlG, KaraaliG. Spanning sets for Möbius vertex algebras satisfying arbitrary difference conditions. J Algebra, 2008, 320: 3345-3364
|
4 |
DongC Y, HanJ Z. Some finite properties for vertex operator superalgebras. Pacific J Math, 2012, 258: 269-290
|
5 |
DongC Y, HanJ Z. On rationality of vertex operator superalgebras. Int Math Res Not,
|
6 |
DongC Y, LiH S, MasonG. Twisted representations of vertex operator algebras. Math Ann, 1998, 310: 571-600
|
7 |
DongC Y, LiH S, MasonG. Vertex operator algebras and associative algebras. J Algebra, 1998, 206: 67-96
|
8 |
DongC Y, RenL. Representations of vertex operator algebras and bimodules. J Algebra, 2013, 384: 212-226
|
9 |
DongC Y, ZhaoZ P. Modularity in orbifold theory for vertex operator superalgebras. Comm Math Phys, 2005, 260: 227-256
|
10 |
FrenkelI B, HuangY-Z, LepowskyJ. On Axiomatic Approaches to Vertex Operator Algebras and Modules. Mem Amer Math Soc, Vol 104, No 494. Providence: Amer Math Soc, 1993
|
11 |
FrenkelI B, ZhuY C. Vertex operator algebras associated to representations of affine and Virasoro algebras. Duke Math J, 1992, 66: 123-168
|
12 |
GaberdielM, NeitzkeA. Rationality, quasirationality and finite W-algebras. Comm Math Phys, 2003, 238: 305-331
|
13 |
HuangY Z. Cofiniteness conditions, projective covers and the logarithmic tensor product theory. J Pure Appl Algebra, 2009, 213: 458-475
|
14 |
HuangY Z, LepowskyJ. A theory of tensor products for module categories for a vertex operator algebra, I. Selecta Math, 1995, 1: 699-756
|
15 |
HuangY Z, LepowskyJ. A theory of tensor products for module categories for a vertex operator algebra, III. J Pure Appl Algebra, 1995, 100: 141-171
|
16 |
HuangY Z, LepowskyJ, ZhangL. Logarithmic tensor product theory for generalized modules for a conformal vertex algebra. arXiv: 0710.2687
|
17 |
HuangY Z, YangJ W. Logarithmic intertwining operators and associative algebras. J Pure Appl Algebra, 2012, 216: 1467-1492
|
18 |
LiH S. Representation Theory and Tensor Product Theory for Vertex Operator Algebras. Ph D Thesis, Rutgers University, 1994
|
19 |
LiH S. Local systems of vertex operators, vertex superalgebras and modules. J Pure Appl Algebra, 1996, 109: 143-195
|
20 |
LiH S. Some finiteness properties of regular vertex operator algebras. J Algebra, 1999, 212: 495-514
|
21 |
MilasA. Weak modules and logarithmic intertwining operators for vertex operator algebras. In: BermanS, FendleyP, HuangY-Z, et al, eds. Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory. Contemp Math, Vol 297. Providence: Amer Math Soc, 2002, 201-225
|
22 |
MiyamotoM. Modular invariance of vertex operator algebras satisfying C2-cofiniteness. Duke Math J, 2004, 122: 51-91
|
23 |
YamauchiH. Modularity on vertex operator algebras arising from semisimple primary vectors. Internat J Math, 2004, 15: 87-109
|
24 |
ZhuY C. Modular invariance of characters of vertex operator algebras. J Amer Math Soc, 1996, 9: 237-302
|
/
〈 | 〉 |