Deformations of algebroid stacks

Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris

Deformations of algebroid stacks

Authors

Bressler, Paul

Gorokhovsky, Alexander

Nest, Ryszard

Tsygan, Boris

Description

In this paper we consider deformations of an algebroid stack on an etale groupoid. We construct a differential graded Lie algebra (DGLA) which controls this deformation theory. In the case when the algebroid is a twisted form of functions we show that this DGLA is quasiisomorphic to the twist of the DGLA of Hochschild cochains on the algebra of functions on the groupoid by the characteristic class of the corresponding gerbe.