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This article is cited in 17 scientific papers (total in 17 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.
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
Linking options:
https://www.mathnet.ru/eng/smj2957 https://www.mathnet.ru/eng/smj/v59/i1/p95
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Abstract page: | 567 | Full-text PDF : | 176 | References: | 216 | First page: | 192 |
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