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arXiv · 1908.02049

A Larson-Sweedler Theorem for Hopf V-Categories

Mitchell Buckley·Timmy Fieremans·Christina Vasilakopoulou·Joost Vercruysse
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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.

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Mitchell Buckley, Timmy Fieremans, Christina Vasilakopoulou, Joost Vercruysse. 2019-08-06. A Larson-Sweedler Theorem for Hopf V-Categories. https://arxiv.org/abs/1908.02049

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