Traces, unitary characters and crossed products by \(\mathbb{Z}\)
type: Item
instance of: scholarly article
title: Traces, unitary characters and crossed products by \(\mathbb{Z}\)
zbMATH Open document ID: 0853.46073
author: Klaus Thomsen
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1997-01-05T00:00:00Z
review text: Summary: We determine the character group of the infinite unitary group of a unital exact \(C^*\)-algebra in terms of K-theory and traces and obtain a description of the infinite unitary group modulo the closure of its commutator subgroup by the same means. The methods are then used to decide when the state space \(SK_0(A\times_\alpha \mathbb{Z})\) of the \(K_0\) group of a crossed product by \(\mathbb{Z}\) is homeomorphic to \(SK_0(A)_{\alpha_*}\) or \(T(A)_\alpha\). We also consider the crossed product \(A\times_\alpha G\) by a discrete countable Abelian group \(G\) and give necessary and sufficient conditions for the equality \(T(A\times_\alpha G)= T(A)_\alpha\) to hold.
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 906880
zbMATH Keywords: unital exact \(C^*\)-algebra
zbMATH Keywords: K-theory
zbMATH Keywords: commutator subgroup
zbMATH Keywords: crossed product
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195163594
OpenAlex ID: W1968543398
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DOI: 10.2977/PRIMS/1195163594
description: scientific article; zbMATH DE number 906880