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C*-crossed products and shift spaces

Silvestrov, Sergei LU and Carlsen, Toke Meier (2007) In Expositiones Mathematicae 25(4). p.275-307
Abstract
We use Exel's C*-crossed products associated to non-invertible dynamical systems to associate a C*-algebra to arbitrary shift space. We show that this C*-algebra is canonically isomorphic to the C*-algebra associated to a shift space given by Carlsen [Cuntz–Pimsner C*-algebras associated with subshifts, Internat. J. Math. (2004) 28, to appear, available at arXiv:math.OA/0505503], has the

C*-algebra defined by Carlsen and Matsumoto [Some remarks on the C*-algebras associated with subshifts, Math. Scand. 95 (1) (2004) 145–160] as a quotient, and possesses properties indicating that it can be thought of as the universal C*-algebra associated to a shift space.



We also consider its representations and its... (More)
We use Exel's C*-crossed products associated to non-invertible dynamical systems to associate a C*-algebra to arbitrary shift space. We show that this C*-algebra is canonically isomorphic to the C*-algebra associated to a shift space given by Carlsen [Cuntz–Pimsner C*-algebras associated with subshifts, Internat. J. Math. (2004) 28, to appear, available at arXiv:math.OA/0505503], has the

C*-algebra defined by Carlsen and Matsumoto [Some remarks on the C*-algebras associated with subshifts, Math. Scand. 95 (1) (2004) 145–160] as a quotient, and possesses properties indicating that it can be thought of as the universal C*-algebra associated to a shift space.



We also consider its representations and its relationship to other C*-algebras associated to shift spaces. We show that it can be viewed as a generalization of the universal Cuntz–Krieger algebra, discuss uniqueness and present a faithful representation, show that it is nuclear and satisfies the Universal Coefficient Theorem, provide conditions for it being simple and purely infinite, show that the constructed C*-algebras and thus their K-theory, K0 and K1, are conjugacy invariants of one-sided shift spaces, present formulas for those invariants, and present a description of the structure of gauge invariant ideals. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Invariants, K-theory, Dynamical systems, Shift spaces, Cuntz–Krieger algebras, C*-algebra
in
Expositiones Mathematicae
volume
25
issue
4
pages
275 - 307
publisher
Urban & Fischer Verlag
external identifiers
  • wos:000250841900001
  • scopus:34948823961
ISSN
0723-0869
DOI
10.1016/j.exmath.2007.02.004
project
Non-commutative Geometry in Mathematics and Physics
Non-commutative Analysis of Dynamics, Fractals and Wavelets
language
English
LU publication?
yes
id
e8d5734a-b3fe-4962-9e30-a4b70d330ffd (old id 939133)
alternative location
http://www.sciencedirect.com/science/journal/07230869
http://www.elsevier.de/exmath
date added to LUP
2008-01-22 13:13:37
date last changed
2017-05-14 04:11:08
@article{e8d5734a-b3fe-4962-9e30-a4b70d330ffd,
  abstract     = {We use Exel's C*-crossed products associated to non-invertible dynamical systems to associate a C*-algebra to arbitrary shift space. We show that this C*-algebra is canonically isomorphic to the C*-algebra associated to a shift space given by Carlsen [Cuntz–Pimsner C*-algebras associated with subshifts, Internat. J. Math. (2004) 28, to appear, available at arXiv:math.OA/0505503], has the <br/><br>
C*-algebra defined by Carlsen and Matsumoto [Some remarks on the C*-algebras associated with subshifts, Math. Scand. 95 (1) (2004) 145–160] as a quotient, and possesses properties indicating that it can be thought of as the universal C*-algebra associated to a shift space.<br/><br>
<br/><br>
We also consider its representations and its relationship to other C*-algebras associated to shift spaces. We show that it can be viewed as a generalization of the universal Cuntz–Krieger algebra, discuss uniqueness and present a faithful representation, show that it is nuclear and satisfies the Universal Coefficient Theorem, provide conditions for it being simple and purely infinite, show that the constructed C*-algebras and thus their K-theory, K0 and K1, are conjugacy invariants of one-sided shift spaces, present formulas for those invariants, and present a description of the structure of gauge invariant ideals.},
  author       = {Silvestrov, Sergei and Carlsen, Toke Meier},
  issn         = {0723-0869},
  keyword      = {Invariants,K-theory,Dynamical systems,Shift spaces,Cuntz–Krieger algebras,C*-algebra},
  language     = {eng},
  number       = {4},
  pages        = {275--307},
  publisher    = {Urban & Fischer Verlag},
  series       = {Expositiones Mathematicae},
  title        = {C*-crossed products and shift spaces},
  url          = {http://dx.doi.org/10.1016/j.exmath.2007.02.004},
  volume       = {25},
  year         = {2007},
}