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arXiv · 1701.08411

A cellular algebra with specific decomposition of the unity

Mufida M. Hmaida
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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 describe the entire Loewy structure of cell modules of the algebra $ \mathbb{A} $ by using the representation theory 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.

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BibTeXRIS

Mufida M. Hmaida. 2017-01-29. A cellular algebra with specific decomposition of the unity. https://arxiv.org/abs/1701.08411

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