Commutative exact algebras and modular tensor categories
Quantum Algebra
2025-12-24 v2 Category Theory
Representation Theory
Abstract
Inspired by the study of vertex operator algebra extensions, we answer the question of when the category of local modules over a commutative exact algebra in a braided finite tensor category is a (non-semisimple) modular tensor category. Along the way we provide sufficient conditions for the category of local modules to be rigid, pivotal and ribbon. We also discuss two ways to construct such commutative exact algebras. The first is the class of simple current algebras and the second is using right adjoints of central tensor functors. Furthermore, we discuss Witt equivalence and its relation with extensions of VOAs.
Cite
@article{arxiv.2408.06314,
title = {Commutative exact algebras and modular tensor categories},
author = {Kenichi Shimizu and Harshit Yadav},
journal= {arXiv preprint arXiv:2408.06314},
year = {2025}
}
Comments
v2: 54 pages. Lemma 5.7 from v1 was incorrect and has been removed. Section 7 has been extensively rewritten