A cellular algebra with specific decomposition of the unity

2017/01/29 by Hmaida, Mufida M.
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1701.08411

Abstract

Let \mathbbA be a cellular algebra over a field \mathbbF with a decomposition of the identity 1_\mathbbA into orthogonal idempotents e_i, i ∈ I (for some finite set I) satisfying some properties. We describe the entire Loewy structure of cell modules of the algebra \mathbbA by using the representation theory of the algebra e_i \mathbbA e_i for each i . Moreover, we also study the block theory of \mathbbA by using this decomposition.

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