Dynamical Systems Associated with Crossed Products
(2007) In LUTFMA-5088-2007/1-13/(2007)- 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:
http://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- unpublished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
- LUTFMA-5088-2007/1-13/(2007)
- issue
- 22
- pages
- 13 pages
- 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
- 2016-08-30 11:24:58
@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}, series = {LUTFMA-5088-2007/1-13/(2007)}, title = {Dynamical Systems Associated with Crossed Products}, year = {2007}, }