THE C*-ALGEBRA OF A TWISTED GROUPOID EXTENSION

Jean N Renault (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

This article extends the main results of [10] to the case of a twisted groupoid. More precisely, it gives a decomposition of the C*-algebra of a twisted locally compact groupoid with Haar system in presence of a normal subgroupoid. When the normal subgroupoid and the twist over it are abelian, one obtains another twisted groupoid C*-algebra. This is applied to C*-algebraic deformation quantization and to multiplier representations of locally compact abelian groups.

Keywords: groupoid extension twist Mackey machine multiplier representation; groupoid extension; twist; Mackey machine; multiplier representation

Domains: Operator Algebras [math.OA]

Jean N Renault. THE C*-ALGEBRA OF A TWISTED GROUPOID EXTENSION. 2022. ⟨hal-03903936⟩