2007/09/19 by Rachel A. D. Martins, Martins, Rachel A. D.
Mathematics · Physics and Astronomy · #16B99 #Advanced Operator Algebra Research #Algebra over a field #Algebraic structures and combinatorial models #Bundle #Double groupoid #FOS: Physical sciences #Fell #Geography #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Mathematics #Noncommutative geometry #Pure mathematics #math-ph #math.MP #msc:16B99
paper · pdf · doi:10.48550/arxiv.0709.2972
Withdrawn to allow for a complete new submission thanks to the addition of other authors.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
openalex publication_date 2007/09/19 · arxiv created 2013/04/17 · arxiv updated 2013/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.