A Larson-Sweedler theorem for Hopf V-categories

Timmy Fieremans, Mitchell Buckley, Christina Vasilakopoulou, Joost Vercruysse

Research output: Contribution to journalArticle

Abstract

The aim of this paper is to extend the classical Larson-Sweedler theorem, namely that a k-bialgebra has a non-singular integral (and in particular is Frobenius) if and only if it is a finite dimensional Hopf algebra, to the ‘many-object’ setting of Hopf categories. To this end, we provide new characterizations of Frobenius V-categories and we develop the integral theory for Hopf V-categories. Our results apply to Hopf algebras in any braided monoidal category as a special case, and also relate to Turaev's Hopf group algebras and particular cases of weak and multiplier Hopf algebras.

Original languageEnglish
Article number107456
Number of pages64
JournalAdvances in Mathematics
Volume376
DOIs
Publication statusPublished - 6 Jan 2021

Keywords

  • Hopf CategoryFrobenius categoryEnriched categoryMonoidal categoryIntegral spaceHopf module

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