The primitivity of semigroup algebras of free products
type: Item
instance of: scholarly article
title: The primitivity of semigroup algebras of free products
zbMATH Open document ID: 0870.16018
DOI: 10.1007/BF02676603
author: Juan-Miguel Gracia
published in: Semigroup Forum
publication date: 1997-07-13T00:00:00Z
full work available at URL: https://eudml.org/doc/135521
review text: Let \(S\) be the free product of semigroups \(A\), \(B\). It is well known that the semigroup algebra \(F[S]\) over any field \(F\) is left and right primitive provided that one of \(A\), \(B\) is nontrivial. In this paper a faithful irreducible representation of \(F[S]\) is constructed. The same is done in the more difficult case of the algebra \(\ell^1(S)\) of infinite sums \(\sum^\infty_{i=1}\alpha_is_i\), \(s_i\in S\), \(\alpha_i\in K\), satisfying \(\sum_i|\alpha_i|<\infty\), over the field \(K\) of reals or complexes. The method is similar to that used by the third author [in Bull. Lond. Math. Soc. 8, 294-298 (1976; Zbl 0344.20002)].
Mathematics Subject Classification ID: 16S36
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 20M30
Mathematics Subject Classification ID: 43A20
zbMATH DE Number: 994597
zbMATH Keywords: free products of semigroups
zbMATH Keywords: semigroup algebras
zbMATH Keywords: faithful irreducible representations
reviewed by: Jan Okniński
MaRDI profile type: Publication
cites work: The Banach algebra \(\ell^1(S)\)
cites work: Group rings of free products are primitive
cites work: The primitivity of free products of associative algebras
cites work: A Representation for l 1 (S )
cites work: On the Primitivity of the Group Ring of a Free Group
OpenAlex ID: W2037391602
description: scientific article; zbMATH DE number 994597