Primitive orthogonal idempotents for \(R\)-trivial monoids.
type: Item
instance of: scholarly article
title: Primitive orthogonal idempotents for \(R\)-trivial monoids.
zbMATH Open document ID: 1252.20053
author: Chris Berg
author: Nantel Bergeron
author: Sandeep Bhargava
author: Franco Saliola
published in: Journal of Algebra
publication date: 2012-04-30T00:00:00Z
full work available at URL: https://arxiv.org/abs/1009.4943
review text: A monoid \(S\) is said to be \(R\)-trivial if Green's relation \(\mathcal R\) is equal to the identity relation. The so called weakly ordered monoids were introduced by \textit{M. Schocker} [J. Algebr. Comb. 28, No. 1, 231-234 (2008; Zbl 1175.20054)] in order to generalize simultaneously 0-Hecke monoids and left regular bands. The problem was to find a complete system of orthogonal idempotents for the corresponding monoid algebras. Every weakly ordered monoid is an \(R\)-trivial monoid. It is proved that for finite monoids the inverse proposition is also true. This fact is used to build a recursive formula for a complete system of primitive orthogonal idempotents for any \(R\)-trivial monoid.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 20M25
zbMATH DE Number: 6029104
zbMATH Keywords: weakly ordered monoids
zbMATH Keywords: 0-Hecke algebras
zbMATH Keywords: left regular bands
zbMATH Keywords: primitive orthogonal idempotents
zbMATH Keywords: representations
zbMATH Keywords: monoid algebras
reviewed by: Grigori I. Zhitomirski
describes a project that uses: Sage-Combinat
describes a project that uses: SageMath
MaRDI profile type: Publication
OpenAlex ID: W2146755739
arXiv ID: 1009.4943
cites work: Q3999421
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DOI: 10.1016/J.JALGEBRA.2011.10.006
description: scientific article; zbMATH DE number 6029104