Coverings of solenoids and automorphisms of semigroup C*-algebras
The paper deals with finite-sheeted covering mappings onto the C*-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 som...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2018-06-01
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| Series: | Учёные записки Казанского университета. Серия Физико-математические науки |
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| Online Access: | https://kpfu.ru/coverings-of-solenoids-and-automorphisms-of-403637.html |
| Summary: | The paper deals with finite-sheeted covering mappings onto the C*-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 C*-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. |
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| ISSN: | 2541-7746 2500-2198 |