0709.2972 (Rachel A. D. Martins)

Double Fell bundles over discrete double groupoids with folding    [PDF]

Rachel A. D. Martins

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.

View original: http://arxiv.org/abs/0709.2972