Dynamical Systems Associated with Crossed Products
(2007) In Preprints in Mathematical Sciences Abstract
 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... (More)
 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/960060
 author
 Svensson, Christian ; Silvestrov, Sergei ^{LU} and de Jeu, Marcel
 organization
 publishing date
 2007
 type
 Contribution to journal
 publication status
 unpublished
 subject
 keywords
 ideals, commutant, dynamical system, topological dynamics, crossed product algebras, C*algebra
 in
 Preprints in Mathematical Sciences
 issue
 22
 pages
 13 pages
 publisher
 Lund University
 external identifiers

 other:LUTFMA50882007/113/(2007)
 ISSN
 14039338
 project
 Noncommutative Analysis of Dynamics, Fractals and Wavelets
 Noncommutative Geometry in Mathematics and Physics
 language
 English
 LU publication?
 yes
 id
 250f6cd5290e4a0abf14f0fce3efb59d (old id 960060)
 date added to LUP
 20160404 09:31:15
 date last changed
 20181121 20:53:41
@article{250f6cd5290e4a0abf14f0fce3efb59d, abstract = {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.}, author = {Svensson, Christian and Silvestrov, Sergei and de Jeu, Marcel}, issn = {14039338}, language = {eng}, number = {22}, publisher = {Lund University}, series = {Preprints in Mathematical Sciences}, title = {Dynamical Systems Associated with Crossed Products}, year = {2007}, }