C*crossed products and shift spaces
(2007) In Expositiones Mathematicae 25(4). p.275307 Abstract
 We use Exel's C*crossed products associated to noninvertible 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 noninvertible 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 Ktheory, K0 and K1, are conjugacy invariants of onesided shift spaces, present formulas for those invariants, and present a description of the structure of gauge invariant ideals. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/939133
 author
 Silvestrov, Sergei ^{LU} and Carlsen, Toke Meier
 organization
 publishing date
 2007
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Invariants, Ktheory, 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
 07230869
 DOI
 10.1016/j.exmath.2007.02.004
 project
 Noncommutative Geometry in Mathematics and Physics
 Noncommutative Analysis of Dynamics, Fractals and Wavelets
 language
 English
 LU publication?
 yes
 id
 e8d5734ab3fe49629e30a4b70d330ffd (old id 939133)
 alternative location
 http://www.sciencedirect.com/science/journal/07230869
 http://www.elsevier.de/exmath
 date added to LUP
 20080122 13:13:37
 date last changed
 20180529 11:10:14
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