$C^*-$crossed product of groupoid actions on categories
| dc.creator | Li, Han | |
| dc.date | 2007-10-18 | |
| dc.date.accessioned | 2026-07-07T08:37:06Z | |
| dc.date.available | 2026-07-07T08:37:06Z | |
| dc.description | Suppose that $G$ is a groupoid acting on a small category $H$ in the sense of \cite[Definition 4]{NOT} and $H\times_αG$ is the resulting semi-direct product category (as in \cite[Proposition 8]{NOT}). We show that there exists a subcategory $H_r \subseteq H$ satisfying some nice property called ``regularity'' such that $H_r \times_αG = H\times_αG$. Moreover, we show that there exists a so-called ``quasi action'' (see Definition \ref{quasi}) $β$ of $G$ on $C^*(H_r)$ (where $C^*(H_r)$ is the semigroupoid $C^*$-algebra as defined in \cite{EXE}) such that $C^*(H_r\times_αG) = C^*(H_r)\times_βG$ (where the crossed product for $β$ is as defined in Definition \ref{cross}). | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0710.3521 | |
| dc.identifier | http://arxiv.org/abs/0710.3521 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140284 | |
| dc.subject | Operator Algebras | |
| dc.subject | Category Theory | |
| dc.subject | 46L05; 18B40 | |
| dc.title | $C^*-$crossed product of groupoid actions on categories | |
| dc.type | text |