Nicolas M. Thiéry - Cartan invariant matrices for finite monoids

dmtcs:3091 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3091
Cartan invariant matrices for finite monoids

Authors: Nicolas M. Thiéry ORCID-iD1

  • 1 Laboratoire de Mathématiques d'Orsay

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.


Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: representation theory of finite monoids, Cartan invariant matrix, characters, computation,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Linked publications - datasets - softwares

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
  • 10.46298/dmtcs.2896
  • 10.46298/dmtcs.2896
  • 1009.4943
  • 10.1016/j.jalgebra.2011.10.006
  • 10.48550/arxiv.1009.4943
Primitive orthogonal idempotents for R-trivial monoids

1 Document citing this article

Consultation statistics

This page has been seen 184 times.
This article's PDF has been downloaded 418 times.