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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 2, Pages 76–82
DOI: https://doi.org/10.26907/0021-3446-2022-2-76-82 (Mi ivm9752) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Brief communications

On a class of local groups and their representations

S. A. Grigoryana, A. Yu. Kuznetsovab

a Kazan State Energy University, 51 Krasnoselskaya str., Kazan, 420066 Russia
b Kazan Federal University, 18 Kremlevskaya str., Kazan, 420008 Russia
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DOI: https://doi.org/10.26907/0021-3446-2022-2-76-82
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.
Received: 04.10.2021
Revised: 04.10.2021
Accepted: 23.12.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 2, Pages 64–69
DOI: https://doi.org/10.3103/S1066369X22020037
Document Type: Article
UDC: 517.98
Language: Russian
Citation: S. A. Grigoryan, A. Yu. Kuznetsova, “On a class of local groups and their representations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 2, 76–82; Russian Math. (Iz. VUZ), 66:2 (2022), 64–69
Citation in format AMSBIB
\Bibitem{GriKuz22}
\by S.~A.~Grigoryan, A.~Yu.~Kuznetsova
\paper On a class of local groups and their representations
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 2
\pages 76--82
\mathnet{http://mi.mathnet.ru/ivm9752}
\crossref{https://doi.org/10.26907/0021-3446-2022-2-76-82}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 2
\pages 64--69
\crossref{https://doi.org/10.3103/S1066369X22020037}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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