<oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:title>Graphs of $C^*$-correspondences and Fell bundles</dc:title>
<dc:creator>Valentin Deaconu</dc:creator><dc:creator>Alex Kumjian</dc:creator><dc:creator>David Pask</dc:creator><dc:creator>Aidan Sims</dc:creator>
<dc:subject>46L05</dc:subject><dc:subject>$C^*$-algebra</dc:subject><dc:subject>graph algebra</dc:subject><dc:subject>$k$-graph</dc:subject><dc:subject>$C^*$-correspondence</dc:subject><dc:subject>groupoid</dc:subject><dc:subject>Fell bundle</dc:subject><dc:subject>product system</dc:subject><dc:subject>Cuntz-Pimsner algebra</dc:subject>
<dc:description>We define the notion of a $\Lambda$-system of $C^{*}$-correspondences associated to a higher-rank graph $\Lambda$. Roughly speaking, such a system assigns to each vertex of $\Lambda$ a $C^{*}$-algebra, and to each path in $\Lambda$ a $C^{*}$-correspondence in a way which carries compositions of paths to balanced tensor products of $C^{*}$-correspondences. Under some simplifying assumptions, we use Fowler&#39;s technology of Cuntz-Pimsner algebras for product systems of $C^{*}$-correspondences to associate a $C^{*}$-algebra to each $\Lambda$-system. We then construct a Fell bundle over the path groupoid $\mathcal{G}_{\Lambda}$ and show that the $C^{*}$-algebra of the $\Lambda$-system coincides with the reduced cross-sectional algebra of the Fell bundle. We conclude by discussing several examples of our construction arising in the literature.</dc:description>
<dc:publisher>Indiana University Mathematics Journal</dc:publisher>
<dc:date>2010</dc:date>
<dc:type>text</dc:type>
<dc:format>pdf</dc:format>
<dc:identifier>10.1512/iumj.2010.59.3893</dc:identifier>
<dc:source>10.1512/iumj.2010.59.3893</dc:source>
<dc:language>en</dc:language>
<dc:relation>Indiana Univ. Math. J. 59 (2010) 1687 - 1736</dc:relation>
<dc:coverage>state-of-the-art mathematics</dc:coverage>
<dc:rights>http://iumj.org/access/</dc:rights>
</oai_dc:dc>