Double Fell bundles over discrete double groupoids with folding
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.
Cite
@article{arxiv.0709.2972,
title = {Double Fell bundles over discrete double groupoids with folding},
author = {Rachel A. D. Martins},
journal= {arXiv preprint arXiv:0709.2972},
year = {2013}
}
Comments
Withdrawn to allow for a complete new submission thanks to the addition of other authors.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