| Title | C*-crossed products and shift spaces |
| Authors | Sergei Silvestrov, Toke Meier Carlsen |
| Alternative Location | http://www.sciencedirect.co..., Restricted Access |
| Alternative Location | http://www.elsevier.de/exmath, Restricted Access |
| Alternative Location | http://dx.doi.org/10.1016/j... |
| Publication | Expositiones Mathematicae |
| Year | 2007 |
| Volume | 25 |
| Issue | 4 |
| Pages | 275 - 307 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Elsevier |
| Abstract English | 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> 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> 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. |
| Keywords | Invariants, K-theory, Dynamical systems, Shift spaces, Cuntz–Krieger algebras, C*-algebra, |
| ISBN/ISSN/Other | ISSN: 0723-0869 |
Questions: webmaster
Last update: 2013-04-11
Centre for Mathematical Sciences, Box 118, SE-22100, Lund. Telefon: +46 46-222 00 00 (vx)