The system of idempotents and the lattice of \({\mathcal J}\)-classes of reductive algebraic monoids
type: Item
instance of: scholarly article
title: The system of idempotents and the lattice of \({\mathcal J}\)-classes of reductive algebraic monoids
zbMATH Open document ID: 0678.20039
DOI: 10.1016/0021-8693(88)90225-6
author: Lex E. Renner
author: Mohan S. Putcha
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: The authors determine the lattice of \({\mathcal J}\)-classes of a regular algebraic monoid, which has only one non-zero minimal \({\mathcal J}\)-class. There are results on the structure of the set of idempotents of a regular algebraic monoid. Many structural questions are reduced to determining the finite lattice \({\mathcal U}=G\setminus M/G\) of \({\mathcal J}\)-classes, where M is a regular algebraic monoid and G is its unit group. It becomes clear that \({\mathcal U}\) is an important semigrouptheoretic link between irreducible representations of G and the Tits building \(\Delta_ G\) of G.
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 4110954
zbMATH Keywords: lattice of \({\mathcal J}\)-classes
zbMATH Keywords: regular algebraic monoid
zbMATH Keywords: idempotents
zbMATH Keywords: unit group
zbMATH Keywords: irreducible representations
zbMATH Keywords: Tits building
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90225-6
OpenAlex ID: W1970957731
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description: scientific article; zbMATH DE number 4110954