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Limits of Inductive Sequences of Toeplitz–Cuntz Algebras

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Abstract

We consider inductive sequences of Toeplitz–Cuntz algebras. The connecting homomorphisms of such a sequence are defined by a finite set of sequences of positive integers. We prove that the inductive limit of such a sequence of Toeplitz–Cuntz algebras is isomorphic to the reduced semigroup \(C^*\)-algebra constructed for the unitalization of the free product of a finite family of semigroups of positive rational numbers. We show that the limit of the inductive sequence of Toeplitz–Cuntz algebras defined by a finite set of sequences of positive integers is a simple \(C^*\)-algebra.

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Funding

This work was performed in the framework of the development program of the Volga Region Scientific–Educational Centre of Mathematics (contract no. 075-02-2020-1478).

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Authors and Affiliations

  1. Kazan State Power Engineering University, Krasnoselskaya ul. 51, Kazan, 420066, Russia

    S. A. Grigoryan & E. V. Lipacheva

  2. N. I. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya ul. 35, Kazan, 420008, Russia

    R. N. Gumerov

Authors
  1. S. A. Grigoryan
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  2. R. N. Gumerov
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  3. E. V. Lipacheva
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Corresponding author

Correspondence to S. A. Grigoryan.

Additional information

Translated from Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 313, pp. 67–77 https://doi.org/10.4213/tm4170.

Translated by I. Nikitin

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Grigoryan, S.A., Gumerov, R.N. & Lipacheva, E.V. Limits of Inductive Sequences of Toeplitz–Cuntz Algebras. Proc. Steklov Inst. Math. 313, 60–69 (2021). https://doi.org/10.1134/S0081543821020073

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  • DOI: https://doi.org/10.1134/S0081543821020073

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