Deformations of algebroid stacks

Paul Bressler; Alexander Gorokhovsky; Ryszard Nest; Boris Tsygan

doi:10.1016/j.aim.2010.10.008

Deformations of algebroid stacks

Paul Bressler, Alexander Gorokhovsky, Ryszard Nest, Boris Tsygan

Department of Mathematical Sciences

7 Citations (Scopus)

Abstract

In this paper we consider deformations of an algebroid stack on an étale 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.

Original language	English
Journal	Advances in Mathematics
Volume	226
Issue number	4
Pages (from-to)	3013-3087
ISSN	0001-8708
DOIs	https://doi.org/10.1016/j.aim.2010.10.008
Publication status	Published - 1 Mar 2011

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10.1016/j.aim.2010.10.008

Cite this

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title = "Deformations of algebroid stacks",

abstract = "In this paper we consider deformations of an algebroid stack on an {\'e}tale 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.",

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AU - Gorokhovsky, Alexander

AU - Nest, Ryszard

AU - Tsygan, Boris

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N2 - In this paper we consider deformations of an algebroid stack on an étale 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.

AB - In this paper we consider deformations of an algebroid stack on an étale 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.

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DO - 10.1016/j.aim.2010.10.008

M3 - Journal article

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VL - 226

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JO - Advances in Mathematics

JF - Advances in Mathematics

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