Graded Brauer groups of a groupoid with involutionReport as inadecuate

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1 Analyse IECL - Institut Élie Cartan de Lorraine 2 LMAM - Laboratoire de Mathématiques et Applications de Metz

Abstract : We define a group BrRG containing, in a sense, the graded complex and orthogonal Brauer groups of a locally compact groupoid G equipped with an involution. When the involution is trivial, we show that the new group naturally provides a generalisation 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 BrRG identifies with a direct sum of a Real cohomology group and the abelian group ExtRG, S 1 of Real graded S 1-central extensions. A cohomological picture is then given.

Author: Elkaioum Moutuou -



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