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Dynamical Systems Associated with Crossed Products

Svensson, Christian; Silvestrov, Sergei LU and de Jeu, Marcel (2007) In Preprints in Mathematical Sciences1999-01-01+01:00
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)
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author
organization
publishing date
type
Contribution to journal
publication status
unpublished
subject
keywords
ideals, commutant, dynamical system, topological dynamics, crossed product algebras, C*-algebra
in
Preprints in Mathematical Sciences1999-01-01+01:00
issue
22
pages
13 pages
publisher
Lund University
external identifiers
  • Other:LUTFMA-5088-2007/1-13/(2007)
ISSN
1403-9338
project
Non-commutative Geometry in Mathematics and Physics
Non-commutative Analysis of Dynamics, Fractals and Wavelets
language
English
LU publication?
yes
id
250f6cd5-290e-4a0a-bf14-f0fce3efb59d (old id 960060)
date added to LUP
2008-01-28 14:50:38
date last changed
2016-11-28 15:46:07
@misc{250f6cd5-290e-4a0a-bf14-f0fce3efb59d,
  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         = {1403-9338},
  keyword      = {ideals,commutant,dynamical system,topological dynamics,crossed product algebras,C*-algebra},
  language     = {eng},
  number       = {22},
  pages        = {13},
  publisher    = {ARRAY(0x8c23290)},
  series       = {Preprints in Mathematical Sciences1999-01-01+01:00},
  title        = {Dynamical Systems Associated with Crossed Products},
  year         = {2007},
}