Tensor categories of affine Lie algebras beyond admissible levels
Creutzig T, Yang J (2021)
Publication Type: Journal article
Publication year: 2021
Journal
Book Volume: 380
Pages Range: 1991-2040
Journal Issue: 3-4
DOI: 10.1007/s00208-021-02159-w
Abstract
We show that if V is a vertex operator algebra such that all the irreducible ordinary V-modules are C1-cofinite and all the grading-restricted generalized Verma modules for V are of finite length, then the category of finite length generalized V-modules has a braided tensor category structure. By applying the general theorem to the simple affine vertex operator algebra (resp. superalgebra) associated to a finite simple Lie algebra (resp. Lie superalgebra) g at level k and the category KLk(g) of its finite length generalized modules, we discover several families of KLk(g) at non-admissible levels k, having braided tensor category structures. In particular, KLk(g) has a braided tensor category structure if the category of ordinary modules is semisimple or more generally if the category of ordinary modules is of finite length. We also prove the rigidity and determine the fusion rules of some categories KLk(g) , including the category KL- 1(sln). Using these results, we construct a rigid tensor category structure on a full subcategory of KL1(sl(n| m)) consisting of objects with semisimple Cartan subalgebra actions.
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APA:
Creutzig, T., & Yang, J. (2021). Tensor categories of affine Lie algebras beyond admissible levels. Mathematische Annalen, 380(3-4), 1991-2040. https://doi.org/10.1007/s00208-021-02159-w
MLA:
Creutzig, Thomas, and Jinwei Yang. "Tensor categories of affine Lie algebras beyond admissible levels." Mathematische Annalen 380.3-4 (2021): 1991-2040.
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