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C*-Algebras Generated by Mappings. Criterion of Irreducibility

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Abstract

We study the operator algebra associated with a self-mapping ϕ on a countable set X which can be represented as a directed graph. The algebra is generated by the family of partial isometries acting on the corresponding l2(X). We study the structure of involutive semigroup multiplicatively generated by the family of partial isometries. We formulate the criterion when the algebra is irreducible on the Hilbert space. We consider the concrete examples of operator algebras. In particular, we give the examples of nonisomorphic C*-algebras, which are the extensions by compact operators of the algebra of continuous functions on the unit circle.

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Authors and Affiliations

  1. Kazan State Power Engineering University, ul. Krasnosel’skaya 51, Kazan, 420066, Russia

    S. A. Grigoryan

  2. Kazan Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    A. Yu. Kuznetsova

Authors
  1. S. A. Grigoryan
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  2. A. Yu. Kuznetsova
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Correspondence to S. A. Grigoryan.

Additional information

Original Russian Text © S.A. Grigoryan, A.Yu. Kuznetsova, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 2, pp. 10–22.

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Grigoryan, S.A., Kuznetsova, A.Y. C*-Algebras Generated by Mappings. Criterion of Irreducibility. Russ Math. 62, 7–18 (2018). https://doi.org/10.3103/S1066369X18020020

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