Cuntzlike algebras
Abstract
The usual crossed product construction which associates to the homeomorphism $T$ of the locally compact space $X$ the C$^*$algebra $C^*(X,T)$ is extended to the case of a partial local homeomorphism $T$. For example, the CuntzKrieger algebras are the C$^*$algebras of the onesided Markov shifts. The generalizations of the CuntzKrieger algebras (graph algebras, algebras $O_A$ where $A$ is an infinite matrix) which have been introduced recently can also be described as C$^*$algebras of Markov chains with countably many states. This is useful to obtain such properties of these algebras as nuclearity, simplicity or pure infiniteness. One also gives examples of strong Morita equivalences arising from dynamical systems equivalences.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 1999
 arXiv:
 arXiv:math/9905185
 Bibcode:
 1999math......5185R
 Keywords:

 Mathematics  Operator Algebras;
 46L55;
 43A35 (Primary);
 43A07;
 43A15;
 43A22 (Secondary)
 EPrint:
 18 pages, AMS LaTeX, to appear in the Proceedings of the 17th Conference in Operator Theory at Timisoara