Commutative exact algebras and modular tensor categories

2024/08/12 by Kenichi Shimizu, Shimizu, Kenichi, Harshit Yadav +1 · 2 citations
#Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2408.06314

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.

Cited by

• Frobenius Algebras, Factorization Homology and the Reshetikhin-Turaev Invariants
• Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories

Related

• Exact sequences of tensor categories
• Rigidity and modularity of vertex tensor categories
• Logarithmic tensor category theory, VIII: Braided tensor category structure on categories of generalized modules for a conformal vertex algebra
• Ribbon categories of weight modules for affine \mathfraksl₂ at admissible levels
• Vertex operator algebras, fusion rules and modular transformations