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Commutative exact algebras and modular tensor categories

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arxiv 2408.06314 v3 pith:OLG7DLKO submitted 2024-08-12 math.QA math.CTmath.RT

Kenichi Shimizu , Harshit Yadav This is my paper · ORCID
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keywords categorytensoralgebrascommutativeexactalgebradiscussextensions
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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.

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  1. Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories

    math.QA 2025-06 accept novelty 8.0 of 10

    A finite braided tensor category is fully dualizable in the Morita 4-category of braided pre-tensor categories whenever its symmetric center is separable.

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