Semisimplicity Criteria for algebras with a Jones Basic Construction

TL;DR

This paper introduces a new method to establish semisimplicity criteria applicable to various algebras, including Brauer, BMW, and q-Brauer algebras.

Contribution

It provides a novel approach for determining semisimplicity in a broad class of algebras, expanding the tools available for algebraic analysis.

Findings

Established a new semisimplicity criterion applicable to multiple algebra classes.

Method successfully applied to Brauer, BMW, and q-Brauer algebras.

Enhances understanding of algebra structures via the Jones basic construction.

Abstract

We prove a semisimplicity criterion for a large class of algebras by a new method. This can be applied to Brauer, BMW, and $q$-Brauer algebras.