Skew products and crossed products by coactions
| dc.creator | Kaliszewski, S. | |
| dc.creator | Quigg, John | |
| dc.creator | Raeburn, Iain | |
| dc.date | 1999-01-22 | |
| dc.date.accessioned | 2026-07-07T05:27:38Z | |
| dc.date.available | 2026-07-07T05:27:38Z | |
| dc.description | 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 cross_c 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 cross_c G) is isomorphic to the crossed product C*(E) cross_delta G. This isomorphism is equivariant for the dual action deltahat and a natural action gamma of G on C*(E cross_c G); following results of Kumjian and Pask, we show that C*(E cross_c G) cross_gamma G is isomorphic to C*(E cross_c G) cross_{gamma,r} G, which in turn is isomorphic to C*(E) tensor K(l^2(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. | |
| dc.description | 22 pages, LaTeX2e, uses pb-diagram.sty | |
| dc.identifier | https://arxiv.org/abs/math/9901101 | |
| dc.identifier | http://arxiv.org/abs/math/9901101 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77991 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L55 | |
| dc.title | Skew products and crossed products by coactions | |
| dc.type | text |