C*-crossed products and shift spaces
(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)
Please use this url to cite or link to this publication:
https://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, 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
- 2016-04-01 16:02:31
- date last changed
- 2022-03-30 05:00:28
@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}},
keywords = {{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}},
doi = {{10.1016/j.exmath.2007.02.004}},
volume = {{25}},
year = {{2007}},
}