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Local Groups and Their Representations

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Abstract

In the paper, we apply the notion of local group in the context of operator algebras, and propose C*-algebraic constructions related to local groups. For a local group we define the concepts of *-representation and strong *-representation which are related to each other with the help of the extension of the local group. The structure of local group allows us to define the regular representation, which is a *-representation, and the respective reduced C*-algebra; the latter is graded over the extension of the local group.

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Authors and Affiliations

  1. Kazan State Energy University, 51 Krasnoselskaya str., Kazan, 420066, Russia

    S. A. Grigoryan

  2. Kazan Federal University, 18 Kremlevskaya str., Kazan, 420008, Russia

    A. Yu. Kuznetsova

Authors
  1. S. A. Grigoryan
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  2. A. Yu. Kuznetsova
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Corresponding authors

Correspondence to S. A. Grigoryan or A. Yu. Kuznetsova.

Additional information

Dedicated to Victor Arzumanyan, our colleague and friend.

Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 6, pp. 73–78.

(submitted by A. M. Bikchentaev)

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Grigoryan, S.A., Kuznetsova, A.Y. Local Groups and Their Representations. Russ Math. 64, 63–68 (2020). https://doi.org/10.3103/S1066369X20060092

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  • DOI: https://doi.org/10.3103/S1066369X20060092

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