On unimodular finite tensor categories

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Abstract

Let C be a finite tensor category with simple unit object, let Z(C) denote its monoidal center, and let L and R be a left adjoint and a right adjoint of the forgetful functor U: Z(C) → C. We show that the following conditions are equivalent: (1) C is unimodular, (2) U is a Frobenius functor, (3) L preserves the duality, (4) R preserves the duality, (5) L(1) is self-dual, and (6) R(1) is self-dual, where 1 ∈ C is the unit object. We also give some other equivalent conditions. As an application, we give a categorical understanding of some topological invariants arising from finite-dimensional unimodular Hopf algebras.

LanguageEnglish
Pages277-322
Number of pages46
JournalInternational Mathematics Research Notices
Volume2017
Issue number1
DOIs
StatePublished - 2017
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On unimodular finite tensor categories. / Shimizu, Kenichi.

In: International Mathematics Research Notices, Vol. 2017, No. 1, 2017, p. 277-322.

Research output: Contribution to journalArticle

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