scholarly journals The crossed-product structure of C*-algebras arising from topological dynamical systems

2103 ◽  
Vol 70 (1) ◽  
pp. 191-210
Author(s):  
Cynthia Farthing ◽  
Nura Patani ◽  
Paulette N. Willis
Keyword(s):  
Dynamical Systems ◽  
Product Structure ◽  
Crossed Product ◽  
C Algebras ◽  
Topological Dynamical Systems

The Local Product Structure of Expansive Automorphisms of Solenoids and Their Associated C*-Algebras

1996 ◽  
Vol 48 (4) ◽  
pp. 692-709 ◽  
Author(s):  
Berndt Brenken
Keyword(s):  
Abelian Group ◽  
Dynamical Systems ◽  
Coordinate System ◽  
Finite Type ◽  
Crossed Product ◽  
C Algebras ◽  
Local Product ◽  
Subshifts Of Finite Type ◽  
Canonical Coordinate System ◽  
Canonical Coordinate

AbstractAn explicit description of a hyperbolic canonical coordinate system for an expansive automorphism of a compact connected abelian group is given. These dynamical systems are factors of subshifts of finite type. Some properties of the associated crossed product C*-algebra are discussed. In these examples, the C* -algebras of Ruelle are crossed product algebras.

Characterizations of topological dynamical systems whose transformation group C*-algebras are antiliminal and of type 1

1993 ◽  
Vol 13 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Nobuo Aoki ◽  
Jun Tomiyama
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Metric Space ◽  
Transformation Group ◽  
Irreducible Representations ◽  
Topological Dynamical System ◽  
Compact Metric Space ◽  
C Algebras ◽  
Topological Dynamical Systems

AbstractFor a topological dynamical system Σ = (X, σ) where X is a compact metric space with a single homeomorphism σ, we determine the largest postliminal ideal of the transformation group C*-algebra A(Σ) as the intersection of all kernels of irreducible representations of A(Σ) induced from those recurrent points which are not periodic. The result implies characterizations of topological dynamical systems whose transformation group C*-algebras are anti-liminal and post-liminal, that is, of type 1.

scholarly journals Exel's crossed product for non-unital C*-algebras

2010 ◽  
Vol 149 (3) ◽  
pp. 423-444 ◽  
Author(s):  
NATHAN BROWNLOWE ◽  
IAIN RAEBURN ◽  
SEAN T. VITTADELLO
Keyword(s):  
Dynamical Systems ◽  
Transfer Operator ◽  
Finite Graph ◽  
Crossed Product ◽  
Crossed Products ◽  
Ideal Structure ◽  
Locally Finite ◽  
C Algebras ◽  
Locally Finite Graph ◽  
The Ideal

AbstractWe consider a family of dynamical systems (A, α, L) in which α is an endomorphism of a C*-algebra A and L is a transfer operator for α. We extend Exel's construction of a crossed product to cover non-unital algebras A, and show that the C*-algebra of a locally finite graph can be realised as one of these crossed products. When A is commutative, we find criteria for the simplicity of the crossed product, and analyse the ideal structure of the crossed product.

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