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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, Number 6, Pages 73–78
DOI: https://doi.org/10.26907/0021-3446-2020-6-73-78 (Mi ivm9584) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Brief communications

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 Univercity, 18, Kremlevskaya str., Kazan, 420008 Russia
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DOI: https://doi.org/10.26907/0021-3446-2020-6-73-78
Abstract: In the paper the notion of a local group is applied in the context of operator algebras, and $C^*$-algebraic constructions are proposed related to the local group. For local group we define $*$-representation and strong $*$-representation which are connected by the extension of the local group. Local group allows you to define the regular representation which is a $*$-representation, and the respective reduced $C^*$-algebra, the last is graded over the extension of the local group.
Keywords: Local group, partial isometry, group partial representation, regular representation, graded $C^*$-algebra.
Received: 20.03.2020
Revised: 20.03.2020
Accepted: 25.03.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, Volume 64, Issue 6, Pages 63–68
DOI: https://doi.org/10.3103/S1066369X20060092
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: S. A. Grigoryan, A. Yu. Kuznetsova, “Local groups and their representations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 6, 73–78; Russian Math. (Iz. VUZ), 64:6 (2020), 63–68
Citation in format AMSBIB
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\paper Local groups and their representations
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
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\pages 73--78
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\jour Russian Math. (Iz. VUZ)
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\issue 6
\pages 63--68
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    • This publication is cited in the following 5 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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