Remarks on the Ideal Structure of Fell Bundle C*-Algebras

Details Remarks on the Ideal Structure of Fell Bundle C*-Algebras Remarks on the Ideal Structure of Fell Bundle C*-Algebras

2009-12-06

arxiv.org/abs/0912.1124v1

Mathematics

Operator Algebras

15 Pages

Scientific paper

We show that if $p:\B\to G$ is a Fell bundle over a locally compact groupoid $G$ and that $A=\Gamma_{0}(G^{(0)};\B)$ is the \cs-algebra sitting over $G^{(0)}$, then there is a continuous $G$-action on $\Prim A$ that reduces to the usual action when $\B$ comes from a dynamical system. As an application, we show that if $I$ is a $G$-invariant ideal in $A$, then there is a short exact sequence of \cs-algebras \xymatrix{0\ar[r]&\cs(G,\BI)\ar[r] &\cs(G,\B)\ar[r]&\cs(G,\BqI)\ar[r]&0,} where $\cs(G,\B)$ is the Fell bundle \cs-algebra and $\BI$ and $\BqI$ are naturally defined Fell bundles corresponding to $I$ and $A/I$, respectively. Of course this exact sequence reduces to the usual one for \cs-dynamical systems.

Affiliated with

Also associated with

No associations

Rating

Remarks on the Ideal Structure of Fell Bundle C*-Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Remarks on the Ideal Structure of Fell Bundle C*-Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Remarks on the Ideal Structure of Fell Bundle C*-Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-84179