The graded Brauer group of a groupoid with involution

Details The graded Brauer group of a groupoid with involution The graded Brauer group of a groupoid with involution

2012-02-09

arxiv.org/abs/1202.2057v1

Mathematics

Functional Analysis

38 pages

Scientific paper

We define a group $\wRBr(\cG)$ containing, in a sense, the graded complex and orthogonal Brauer groups of a locally compact groupoid $\cG$ equipped with an involution. When the involution is trivial, we show that the new group naturally provides a generalization of Donovan-Karoubi's graded orthogonal Brauer group $GBrO$. More generally, it is shown to be a direct summand of the well-known graded complex Brauer goup. In addition, we prove that $\wRBr(\cG)$ identifies with a direct sum of a Real cohomology group and the abelian group $\wRExt(\cG,\uc)$ of Real graded $\uc$-central extensions. A cohomological picture is then given.

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