Integral Theory for Quasi-Hopf Algebras

TL;DR

This paper extends the fundamental structure theorem to quasi-Hopf algebras, establishing the existence and uniqueness of integrals in finite-dimensional cases and applying this to prove a Maschke type theorem.

Contribution

It generalizes the structure theorem for Hopf modules to quasi-Hopf algebras and proves the existence and uniqueness of integrals in finite-dimensional cases.

Findings

Existence and uniqueness of integrals in finite-dimensional quasi-Hopf algebras.

Generalization of the structure theorem for Hopf modules.

Proof of a Maschke type theorem for diagonal crossed products.

Abstract

We generalize the fundamental structure Theorem on Hopf (bi)-modules by Larson and Sweedler to quasi-Hopf algebras H. If H is finite dimensional this proves the existence and uniqueness (up to scalar multiples) of integrals in H. Among other applications we prove a Maschke type Theorem for diagonal crossed products as constructed by the authors.