Double Fell bundles over discrete double groupoids with folding
arXiv:0709.2972
Abstract
In this paper we construct the notions of double Fell bundle and double C*-category for possible future use as tools to describe noncommutative spaces, in particular in finite dimensions. We identify the algebra of sections of a double Fell line bundle over a discrete double groupoid with folding with the convolution algebra of the latter. This turns out to be what one might call a double C*-algebra. We generalise the Gelfand-Naimark-Segal construction to double C*-categories and we form the dual category for a saturated double Fell bundle using the Tomita-Takesaki involution.
Withdrawn to allow for a complete new submission thanks to the addition of other authors. In preparation: "Involutive double categories" with Bertozzini, Conti and Resende
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