$C^*-$crossed product of groupoid actions on categories

dc.creatorLi, Han
dc.date2007-10-18
dc.date.accessioned2026-07-07T08:37:06Z
dc.date.available2026-07-07T08:37:06Z
dc.descriptionSuppose 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.description14 pages
dc.identifierhttps://arxiv.org/abs/0710.3521
dc.identifierhttp://arxiv.org/abs/0710.3521
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140284
dc.subjectOperator Algebras
dc.subjectCategory Theory
dc.subject46L05; 18B40
dc.title$C^*-$crossed product of groupoid actions on categories
dc.typetext

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