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Discrete Mathematics & Theoretical Computer Science |
Let $M$ be a finite monoid. In this paper we describe how the Cartan invariant matrix of the monoid algebra of $M$ over a field $\mathbb{K}$ of characteristic zero can be expressed using characters and some simple combinatorial statistic. In particular, it can be computed efficiently from the composition factors of the left and right class modules of $M$. When $M$ is aperiodic, this approach works in any characteristic, and generalizes to $\mathbb{K}$ a principal ideal domain like $\mathbb{Z}$. When $M$ is $\mathcal{R}$-trivial, we retrieve the formerly known purely combinatorial description of the Cartan matrix.
Source : ScholeXplorer
IsRelatedTo ARXIV 1009.4943 Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.jalgebra.2011.10.006 Source : ScholeXplorer IsRelatedTo DOI 10.46298/dmtcs.2896 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1009.4943
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