This article is cited in 1 paper

Brief communications

On a class of local groups and their representations

S. A. Grigoryan^a, A. Yu. Kuznetsova<sup>b

a</sup> Kazan State Energy University, 51 Krasnoselskaya str., Kazan, 420066 Russia
^b Kazan Federal University, 18 Kremlevskaya str., Kazan, 420008 Russia

Abstract: In the work the authors propose to apply the notion of a local group in the theory of $C^*$-algebras. The regular representation is defined, which is a $*$-representation and generates the reduced $C^*$-algebra. A class of local groups is constructed, generated by the subset $P$ of a discrete group, for which the notion of the $P$-regular representation is defined, which is a strong $*$-representation and generates the corresponding reduced algebra. Examples of simple algebras are given, constructed from given subsets of an abelian group.

Keywords: local group, partial isometry, regular representation, graded $C^*$-algebra, $UHF$-algebra, $AF$-algebra.

UDC: 517.98

Received: 04.10.2021
Revised: 04.10.2021
Accepted: 23.12.2021

DOI: 10.26907/0021-3446-2022-2-76-82

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2022, 66:2, 64–69