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

Institut for Matematiske Fag

7 Citationer (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.

Originalsprog	Engelsk
Tidsskrift	Advances in Mathematics
Vol/bind	226
Udgave nummer	4
Sider (fra-til)	3013-3087
ISSN	0001-8708
DOI	https://doi.org/10.1016/j.aim.2010.10.008
Status	Udgivet - 1 mar. 2011

Adgang til dokumentet

10.1016/j.aim.2010.10.008

Citationsformater

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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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T1 - Deformations of algebroid stacks

AU - Bressler, Paul

AU - Gorokhovsky, Alexander

AU - Nest, Ryszard

AU - Tsygan, Boris

PY - 2011/3/1

Y1 - 2011/3/1

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.

U2 - 10.1016/j.aim.2010.10.008

DO - 10.1016/j.aim.2010.10.008

M3 - Journal article

SN - 0001-8708

VL - 226

SP - 3013

EP - 3087

JO - Advances in Mathematics

JF - Advances in Mathematics

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