On graded semigroup \(C^*\)-algebras and Hilbert modules
type: Item
instance of: scholarly article
title: On graded semigroup \(C^*\)-algebras and Hilbert modules
zbMATH Open document ID: 1469.46044
DOI: 10.1134/S0081543821020127
author: E. V. Lipacheva
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2021-07-23T00:00:00Z
review text: Let \(S\) be a cancellative semigroup with identity \(e\), \(C^*_r(S)\) its reduced semigroup, \(G\) a group, and let \(\sigma:S\to G\) be a surjective semigroup homomorphism. Then a natural topological \(G\)-grading \(\{\mathfrak A_g:g\in G\}\) is constructed on \(C^*_r(S)\). If \(G\) is finite, then a projective Hilbert \(C^*\)-module structure (over \(\mathfrak A_e\)) is introduced on \(C^*_r(S)\).
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L08
zbMATH DE Number: 7374308
zbMATH Keywords: semigroup \(C^*\)-algebra
zbMATH Keywords: grading
zbMATH Keywords: Hilbert \(C^*\)-module
reviewed by: Vladimir M. Manuilov
MaRDI profile type: Publication
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full work available at URL: s0081543821020127
OpenAlex ID: W3183695956
description: scientific article; zbMATH DE number 7374308