The minimal closed non-trivial ideals of Toeplitz algebras on discrete groups
type: Item
instance of: scholarly article
title: The minimal closed non-trivial ideals of Toeplitz algebras on discrete groups
zbMATH Open document ID: 0967.47044
DOI: 10.1142/S0252959900000388
author: Qingxiang Xu
published in: Chinese Annals of Mathematics. Series B
publication date: 2001-08-27T00:00:00Z
review text: Let \(G\) be a discrete, not necessary abelian, group and \(G_+\) be a subset of \(G\), such that \((G,G_+)\) be an ordered group. Let \(G_g, g\in G_+\backslash\{g\}\) be a semigroup of \(G\) generated by \(G_+\) and \(g^{-1}\) and \(G_F=\bigcap_{g\in G_+\backslash\{e\}}G_g\), so that \((G,G_F)\) be the minimal quasi-group containing \((G,G_+)\). Let also \(\gamma^{G_F,G_+}\) be the natural \(C^\ast\)-algebra morphism from Toeplitz algebra \(T^{G_+} (G)\) to Toeplitz algebra \(T^{G_F} (G)\). It is supposed that the group \(G\) is amenable and \(G_F\neq G_+\). The author shows that \(ker\;\gamma^{G_F,G_+}\) is exactly the minimal closed non-trivial ideal of \(T^{G_+} (G)\). Some applications of this result are also given.
Mathematics Subject Classification ID: 47L80
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 1530106
zbMATH Keywords: Toeplitz algebras
zbMATH Keywords: minimal quasi-group
zbMATH Keywords: \(C^\ast\)-algebra morphism
zbMATH Keywords: discrete group
zbMATH Keywords: ideal
reviewed by: N. Karapetiants
MaRDI profile type: Publication
full work available at URL: s0252959900000388
OpenAlex ID: W2356666247
Wikidata QID: Q129863948
description: scientific article; zbMATH DE number 1530106