Cuntz-like algebras

Details Cuntz-like algebras Cuntz-like algebras

1999-05-29

arxiv.org/abs/math/9905185v1

Mathematics

Operator Algebras

18 pages, AMS LaTeX, to appear in the Proceedings of the 17th Conference in Operator Theory at Timisoara

Scientific paper

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 Cuntz-Krieger algebras are the C$^*$-algebras of the one-sided Markov shifts. The generalizations of the Cuntz-Krieger 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.

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