Profinite pro-C*-algebras and pro-C*-algebras of profinite groups

Details Profinite pro-C*-algebras and pro-C*-algebras of profinite groups Profinite pro-C*-algebras and pro-C*-algebras of profinite groups

2011-10-15

arxiv.org/abs/1110.3411v2

Mathematics

Operator Algebras

18 pages; no figures. Changes from the previous version: Questions 3.14 and 3.15 in the previous version have been answered. I

Scientific paper

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.

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