Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, Volume 160, Book 2, Pages 275–286
Coverings of solenoids and automorphisms of semigroup $C^*$-algebras
R. N. Gumerov
Kazan Federal University, Kazan, 420008 Russia
The paper deals with finite-sheeted covering mappings onto the $P$-adic solenoids and limit endomorphisms of semigroup $C^*$-algebras. The aim of our exposition is two-fold: firstly, to present the results concerning the above-mentioned mappings and endomorphisms; secondly, to demonstrate proofs for some of the results. It has been shown that every covering mapping onto a solenoid is isomorphic to a power mapping. We have considered dynamical properties of the covering mappings. A power mapping for the $P$-adic solenoid is topologically transitive. A criterion for the covering mapping to be chaotic has been given. The classical Euler–Fermat theorem may be used in its proof. We have studied limit endomorphisms of $C^*$-algebras generated by isometric representations for semigroups of rational numbers. We formulate criteria for limit endomorphisms to be automorphisms in number-theoretic, algebraic, and functional terms. The necessity of such a criterion has been given from the category-theoretic viewpoint.
automorphism of $C^*$-algebras, chaotic, inductive sequence of Toeplitz algebras associated with sequence of prime numbers, inverse limit and sequence, finite-sheeted covering mapping, semigroup $C^*$-algebra, solenoid, $*$-homomorphism, Toeplitz algebra, topologically transitive.
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R. N. Gumerov, “Coverings of solenoids and automorphisms of semigroup $C^*$-algebras”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 160, no. 2, Kazan University, Kazan, 2018, 275–286
Citation in format AMSBIB
\paper Coverings of solenoids and automorphisms of semigroup $C^*$-algebras
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\publ Kazan University
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