Profinite pro-C*-algebras and pro-C*-algebras of profinite groups
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Publication:2938873
zbMATH Open1319.46042arXiv1110.3411MaRDI QIDQ2938873
Author name not available (Why is that?)
Publication date: 16 January 2015
Abstract: We define the profinite completion of a C*-algebra, which is a pro-C*-algebra, as well as the pro-C*-algebra of a profinite group. We show that the continuous representations of the pro-C*-algebra of a profinite group correspond to the unitary representations of the group which factor through a finite group. We define natural homomorphisms from the C*-algebra of a locally compact group and its profinite completion to the pro-C*-algebra of the profinite completion of the group. We give some conditions for injectivity or surjectivity of these homomorphisms, but an important question remains open.
Full work available at URL: https://arxiv.org/abs/1110.3411
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