A cellular algebra with specific decomposition of the unity

Abstract

Let $\mathbb{A}$ be a cellular algebra over a field $\mathbb{F}$ with a decomposition of the identity $1_{\mathbb{A}}$ into orthogonal idempotents $e_i,i\in I$ (for some finite set I) satisfying some properties. We present a technique to describe the radical and the head of each cell module of the algebra $\mathbb{A}$ by using the cell modules of the algebra $e_i\mathbb{A}{e}_i$ for each i. Moreover, we also study the block theory of $\mathbb{A}$ by using this decomposition.

Keywords:

• Cellular algebra
• Levi-type sub-algebra
• multi-color partition algebra

MATHEMATICS SUBJECT CLASSIFICATION:

• 16D70
• 16W10
• 16N20
• 16U99