Semisimplicity of cellular algebras over positive characteristic fields

TL;DR

This paper explores when cellular algebras over fields with positive characteristic are semisimple, showing that the Frame number determines semisimplicity, extending Maschke's theorem.

Contribution

It introduces the Frame number as a key criterion for semisimplicity of cellular algebras over positive characteristic fields, generalizing classical results.

Findings

Frame number characterizes semisimplicity

Generalization of Maschke's theorem

Provides a criterion for cellular algebra semisimplicity

Abstract

In this paper, we investigate semisimplicity of cellular algebras over positive characteristic fields. Our main result shows that the Frame number of cellular algebras characterizes semisimplicity of it. In a sense, this is a generalization of Maschke's theorem.