Semigroupoid C*-Algebras

Details Semigroupoid C*-Algebras Semigroupoid C*-Algebras

2006-11-30

arxiv.org/abs/math/0611929v2

Mathematics

Operator Algebras

25 pages, 12 point type, no figures; Reformulated introduction and abstract. New references. No change in the basic mathematic

Scientific paper

A semigroupoid is a set equipped with a partially defined associative operation. Given a semigroupoid \Lambda we construct a C*-algebra C*(\Lambda) from it. We then present two main examples of semigroupoids, namely the Markov semigroupoid associated to an infinite 0-1 matrix, and the semigroupoid associated to a row-finite higher-rank graph without sources. In both cases the semigroupoid C*-algebra is shown to be isomorphic to the algebras usually attached to the corresponding combinatorial object, namely the Cuntz-Krieger algebras and the higher-rank graph C*-algebras, respectively. In the case of a higher-rank graph (\Lambda,d), it follows that the dimension function d is superfluous for defining the corresponding C*-algebra.

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