Dynamical systems associated with crossed products
| Autor: | Marcel de Jeu, Sergei Silvestrov, Christian Svensson |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Pure mathematics maximal abelian subalgebra Dynamical systems theory Applied Mathematics Mathematics - Operator Algebras Crossed product ideal Dynamical Systems (math.DS) Automorphism dynamical system 47L65 16S35 37B05 54H20 ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Banach algebra FOS: Mathematics Ideal (ring theory) Algebraic number Mathematics - Dynamical Systems Dynamical system (definition) Operator Algebras (math.OA) Commutative property Banach *-algebra Mathematics |
| Zdroj: | Acta Applicandae Mathematicae, 108(3), 547-559 |
| Popis: | In this paper, we consider both algebraic crossed products of commutative complex algebras A with the integers under an automorphism of A, and Banach algebra crossed products of commutative C^*-algebras A with the integers under an automorphism of A. We investigate, in particular, connections between algebraic properties of these crossed products and topological properties of naturally associated dynamical systems. For example, we draw conclusions about the ideal structure of the crossed product by investigating the dynamics of such a system. To begin with, we recall results in this direction in the context of an algebraic crossed product and give simplified proofs of generalizations of some of these results. We also investigate new questions, for example about ideal intersection properties of algebras properly between the coefficient algebra A and its commutant A'. Furthermore, we introduce a Banach algebra crossed product and study the relation between the structure of this algebra and the topological dynamics of a naturally associated system. 13 pages. 2 references addes and minor text improvements made |
| Databáze: | OpenAIRE |
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