A Larson-Sweedler Theorem for Hopf V-Categories
Category Theory
2020-10-19 v3 Rings and Algebras
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.
Keywords
Cite
@article{arxiv.1908.02049,
title = {A Larson-Sweedler Theorem for Hopf V-Categories},
author = {Mitchell Buckley and Timmy Fieremans and Christina Vasilakopoulou and Joost Vercruysse},
journal= {arXiv preprint arXiv:1908.02049},
year = {2020}
}
Comments
54 pages, 1 Table. Revised manuscript according to referees' suggestions. To appear in Advances in Mathematics