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- Title
An sl2-type tensor category for the Virasoro algebra at central charge 25 and applications.
- Authors
McRae, Robert; Yang, Jinwei
- Abstract
Let O 25 be the vertex algebraic braided tensor category of finite-length modules for the Virasoro Lie algebra at central charge 25 whose composition factors are the irreducible quotients of reducible Verma modules. We show that O 25 is rigid and that its simple objects generate a semisimple tensor subcategory that is braided tensor equivalent to an abelian 3-cocycle twist of the category of finite-dimensional sl 2 -modules. We also show that this sl 2 -type subcategory is braid-reversed tensor equivalent to a similar category for the Virasoro algebra at central charge 1. As an application, we construct a simple conformal vertex algebra which contains the Virasoro vertex operator algebra of central charge 25 as a P S L 2 (C) -orbifold. We also use our results to study Arakawa’s chiral universal centralizer algebra of S L 2 at level - 1 , showing that it has a symmetric tensor category of representations equivalent to Rep P S L 2 (C) . This algebra is an extension of the tensor product of Virasoro vertex operator algebras of central charges 1 and 25, analogous to the modified regular representations of the Virasoro algebra constructed earlier for generic central charges by I. Frenkel–Styrkas and I. Frenkel–M. Zhu.
- Subjects
ABELIAN categories; VERTEX operator algebras; UNIVERSAL algebra; SEMISIMPLE Lie groups; ALGEBRA; REPRESENTATIONS of algebras; LIE algebras; TENSOR products
- Publication
Mathematische Zeitschrift, 2023, Vol 303, Issue 2, p1
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-022-03197-z