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Sibirsk. Mat. Zh., 2018, Volume 59, Number 1, Pages 95–109 (Mi smj2957)  

This article is cited in 2 scientific papers (total in 2 papers)

Limit automorphisms of the $C^*$-algebras generated by isometric representations for semigroups of rationals

R. N. Gumerov

Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: We consider inductive sequences of Toeplitz algebras whose connecting homomorphisms are defined by collections of primes. The inductive limits of these sequences are $C^*$-algebras generated by representations for semigroups of rationals. We study the limit endomorphisms of these $C^*$-algebras induced by morphisms between copies of the same inductive sequences of Toeplitz algebras. We establish necessary and sufficient conditions for these endomorphisms to be automorphisms of the algebras.

Keywords: automorphism, Toeplitz algebra, inductive sequence, inductive limit, limit endomorphism, semigroup $C^*$-algebra, semigroup of rationals, sequence of primes, solenoid.

DOI: https://doi.org/10.17377/smzh.2018.59.109

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English version:
Siberian Mathematical Journal, 2018, 59:1, 73–84

Bibliographic databases:

UDC: 517.986
MSC: 35R30
Received: 12.09.2016

Citation: R. N. Gumerov, “Limit automorphisms of the $C^*$-algebras generated by isometric representations for semigroups of rationals”, Sibirsk. Mat. Zh., 59:1 (2018), 95–109; Siberian Math. J., 59:1 (2018), 73–84

Citation in format AMSBIB
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\by R.~N.~Gumerov
\paper Limit automorphisms of the $C^*$-algebras generated by isometric representations for semigroups of rationals
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
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\pages 95--109
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\crossref{https://doi.org/10.17377/smzh.2018.59.109}
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\transl
\jour Siberian Math. J.
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\vol 59
\issue 1
\pages 73--84
\crossref{https://doi.org/10.1134/S0037446618010093}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. N. Gumerov, E. V. Lipacheva, T. A. Grigoryan, “On inductive limits for systems of $C^*$-algebras”, Russian Math. (Iz. VUZ), 62:7 (2018), 68–73  mathnet  crossref  isi
    2. R. N. Gumerov, “Coverings of solenoids and automorphisms of semigroup $C^*$-algebras”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 160, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2018, 275–286  mathnet  mathscinet
  • Сибирский математический журнал Siberian Mathematical Journal
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