Self-injective cellular algebras of polynomial growth representation type

TL;DR

This paper classifies certain self-injective cellular algebras with polynomial growth representation type, focusing on Morita equivalence classes under the assumption of odd characteristic fields, contributing to the understanding of algebra classification.

Contribution

It provides a classification of Morita equivalence classes of indecomposable self-injective cellular algebras with polynomial growth, assuming odd characteristic fields, which was previously unestablished.

Findings

Classification of Morita equivalence classes achieved

Identifies conditions under which cellularity is a Morita invariant

Focuses on algebras over fields with odd characteristic

Abstract

We classify Morita equivalence classes of indecomposable self-injective cellular algebras which have polynomial growth representation type, assuming that the base field has an odd characteristic. This assumption on the characteristic is for the cellularity to be a Morita invariant property.