2006/11/30 by Ruy Exel, Exel, Ruy · 2 citations
Mathematics · #18B40 #46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Operator Algebras (math.OA) #math.CT #math.OA #msc:18B40 #msc:46L05
paper · pdf · doi:10.48550/arxiv.math/0611929
25 pages, 12 point type, no figures; Reformulated introduction and abstract. New references. No change in the basic mathematics
openalex publication_date 2006/11/30 · arxiv created 2007/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A semigroupoid is a set equipped with a partially defined associative operation. Given a semigroupoid Λwe construct a C*-algebra C*(Λ) 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 (Λ,d), it follows that the dimension function d is superfluous for defining the corresponding C*-algebra.