Some computations of Frobenius-Schur indicators of the regular representations of Hopf algebras

TL;DR

This paper computes Frobenius-Schur indicators for regular representations of finite-dimensional semisimple Hopf algebras, especially group-theoretical ones, and explores a Frobenius-type theorem in this context.

Contribution

It provides explicit computations of indicators and formulates a Frobenius theorem for semisimple Hopf algebras, advancing understanding of their representation theory.

Findings

Explicit Frobenius-Schur indicator calculations for various Hopf algebras

Formulation of a Frobenius theorem for semisimple Hopf algebras

Partial results supporting the Frobenius conjecture in this setting

Abstract

We study Frobenius-Schur indicators of the regular representations of finite-dimensional semisimple Hopf algebras, especially group-theoretical ones. Those of various Hopf algebras are computed explicitly. In view of our computational results, we formulate the theorem of Frobenius for semisimple Hopf algebras and give some partial results on this problem.