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^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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 (US)
Pages (from-to)	3018-3087
Number of pages	70
Journal	Advances in Mathematics
Volume	226
Issue number	4
DOIs	https://doi.org/10.1016/j.aim.2010.10.008
State	Published - Mar 1 2011

Funding

* Corresponding author. E-mail addresses: [email protected] (P. Bressler), [email protected] (A. Gorokhovsky), [email protected] (R. Nest), [email protected] (B. Tsygan). 1 Partially supported by NSF grants DMS-0400342 and DMS-0900968. 2 Partially supported by NSF grants DMS-0605030 and DMS-0906391.

Keywords

Algebroid stacks
Deformation quantization
Gerbes

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2010.10.008

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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.",

keywords = "Algebroid stacks, Deformation quantization, Gerbes",

author = "Paul Bressler and Alexander Gorokhovsky and Ryszard Nest and Boris Tsygan",

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AU - Gorokhovsky, Alexander

AU - Nest, Ryszard

AU - Tsygan, Boris

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PY - 2011/3/1

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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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KW - Gerbes

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Deformations of algebroid stacks

Abstract

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Keywords

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