Radicals of symmetric cellular algebras

TL;DR

This paper constructs a nilpotent ideal in finite dimensional symmetric cellular algebras, linking cell module radicals with the algebra's radical and providing insights into simple module dimensions.

Contribution

It introduces a new nilpotent ideal that connects cell module radicals with the algebra's radical, revealing structural information.

Findings

Constructed a nilpotent ideal in symmetric cellular algebras

Connected radicals of cell modules with the algebra's radical

Provided information on dimensions of simple modules

Abstract

Let A be a finite dimensional symmetric cllular algebras. We construct a nilpotent ideal in A. The ideal connects the radicals of cell modules with the radical of the algebra. It also reveals some information on the dimensions of simple modules of A.