Twistings of KR for Real groupoids
K-Theory and Homology
2011-11-01 v1 Mathematical Physics
Algebraic Topology
math.MP
Operator Algebras
Abstract
B-fields over a groupoid with involution are defined as Real graded Dixmier-Douady bundles. We use these to introduce the Real graded Brauer group which constitutes the set of twistings for Atiyah's KR-functor in the category of locally compact groupoids with involutions. We interpret this group in terms of groupoid extensions and elements of some equivariant Cech cohomology theory. The construction of the twisted KR-functor is outlined.
Keywords
Cite
@article{arxiv.1110.6836,
title = {Twistings of KR for Real groupoids},
author = {El-kaïoum M. Moutuou},
journal= {arXiv preprint arXiv:1110.6836},
year = {2011}
}