Representations of Munn algebras and related semigroups

TL;DR

This paper classifies the representation types of finite dimensional Munn algebras with semisimple bases and applies these results to determine the representation types of certain finite semigroups.

Contribution

It provides a comprehensive classification of the representation types of Munn algebras and related semigroups, extending understanding in algebraic representation theory.

Findings

Finite dimensional Munn algebras can be classified as finite, tame, or wild.

Representation types of finite 0-simple semigroups are determined.

Mutually annihilating unions of semigroups have established representation types.

Abstract

We establish representation types (finite, tame or wild) of finite dimensional Munn algebras with semisimple bases. As an application, we establish representation types of finite 0-simple semigroups and their mutually annihilating unions.