1999/01/22 by S. Kaliszewski, John Quigg, Kaliszewski, S. +3 · 5 citations
Mathematics · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L55
paper · pdf · doi:10.48550/arxiv.math/9901101
22 pages, LaTeX2e, uses pb-diagram.sty
arxiv created 1999/01/22 · openalex publication_date 1999/01/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a labeling c of the edges of a directed graph E by elements of a discrete group G, one can form a skew-product graph E crossc G. We show, using the universal properties of the various constructions involved, that there is a coaction delta of G on C*(E) such that C*(E crossc G) is isomorphic to the crossed product C*(E) crossdelta G. This isomorphism is equivariant for the dual action deltahat and a natural action gamma of G on C*(E crossc G); following results of Kumjian and Pask, we show that C*(E crossc G) crossgamma G is isomorphic to C*(E crossc G) crossgamma,r G, which in turn is isomorphic to C*(E) tensor K(l2(G)), and it turns out that the action gamma is always amenable. We also obtain corresponding results for r-discrete groupoids Q and continuous homomorphisms c: Q -> G, provided Q is amenable. Some of these hold under a more general technical condition which obtains whenever Q is amenable or second-countable.