August 2019 Commutator ideals in C-crossed products by hereditary subsemigroups
Mamoon Ahmed
Ann. Funct. Anal. 10(3): 370-380 (August 2019). DOI: 10.1215/20088752-2018-0036

Abstract

Let (G,G+) be a lattice-ordered abelian group with positive cone G+, and let H+ be a hereditary subsemigroup of G+. In previous work, the author and Pryde introduced a closed ideal IH+ of the C-subalgebra BG+ of (G+) spanned by the functions {1x:xG+}. Then we showed that the crossed product C-algebra B(G/H)+×βG+ is realized as an induced C-algebra IndHGˆ(B(G/H)+×τ(G/H)+). In this paper, we prove the existence of the following short exact sequence of C-algebras: 0IH+×αG+BG+×αG+IndHGˆ(B(G/H)+×τ(G/H)+)0. This relates BG+×αG+ to the structure of IH+×αG+ and B(G/H)+×βG+. We then show that there is an isomorphism ι of BH+×αH+ into BG+×αG+. This leads to nontrivial results on commutator ideals in C-crossed products by hereditary subsemigroups involving an extension of previous results by Adji, Raeburn, and Rosjanuardi.

Citation

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Mamoon Ahmed. "Commutator ideals in C-crossed products by hereditary subsemigroups." Ann. Funct. Anal. 10 (3) 370 - 380, August 2019. https://doi.org/10.1215/20088752-2018-0036

Information

Received: 12 September 2018; Accepted: 9 December 2018; Published: August 2019
First available in Project Euclid: 6 August 2019

zbMATH: 07089124
MathSciNet: MR3989182
Digital Object Identifier: 10.1215/20088752-2018-0036

Subjects:
Primary: 46L55
Secondary: 22D25

Keywords: $C^{*}$-algebra , commutator ideal , crossed product , lattice-ordered group

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 3 • August 2019
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