Deformation quantization of gerbes

Paul Bressler; Alexander Gorokhovsky; Ryszard Nest; Boris Tsygan

doi:10.1016/j.aim.2007.02.002

Deformation quantization of gerbes

Paul Bressler, Alexander Gorokhovsky, Ryszard Nest, Boris Tsygan^*

^*Corresponding author for this work

Mathematics

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

32 Scopus citations

Abstract

This is the first in a series of articles devoted to deformation quantization of gerbes. We introduce basic definitions, interpret deformations of a given stack as Maurer-Cartan elements of a differential graded Lie algebra (DGLA), and classify deformations of a given gerbe in terms of Maurer-Cartan elements of the DGLA of Hochschild cochains twisted by the cohomology class of the gerbe. We also classify all deformations of a given gerbe on a symplectic manifold, as well as provide a deformation-theoretic interpretation of the first Rozansky-Witten class.

Original language	English (US)
Pages (from-to)	230-266
Number of pages	37
Journal	Advances in Mathematics
Volume	214
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2007.02.002
State	Published - Sep 10 2007

Funding

The research of A.G. and B.T. was partially supported by NSF grants.

Keywords

Deformation
Quantization

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2007.02.002

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abstract = "This is the first in a series of articles devoted to deformation quantization of gerbes. We introduce basic definitions, interpret deformations of a given stack as Maurer-Cartan elements of a differential graded Lie algebra (DGLA), and classify deformations of a given gerbe in terms of Maurer-Cartan elements of the DGLA of Hochschild cochains twisted by the cohomology class of the gerbe. We also classify all deformations of a given gerbe on a symplectic manifold, as well as provide a deformation-theoretic interpretation of the first Rozansky-Witten class.",

keywords = "Deformation, Quantization",

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AU - Bressler, Paul

AU - Gorokhovsky, Alexander

AU - Nest, Ryszard

AU - Tsygan, Boris

N1 - Funding Information: The research of A.G. and B.T. was partially supported by NSF grants.

PY - 2007/9/10

Y1 - 2007/9/10

N2 - This is the first in a series of articles devoted to deformation quantization of gerbes. We introduce basic definitions, interpret deformations of a given stack as Maurer-Cartan elements of a differential graded Lie algebra (DGLA), and classify deformations of a given gerbe in terms of Maurer-Cartan elements of the DGLA of Hochschild cochains twisted by the cohomology class of the gerbe. We also classify all deformations of a given gerbe on a symplectic manifold, as well as provide a deformation-theoretic interpretation of the first Rozansky-Witten class.

AB - This is the first in a series of articles devoted to deformation quantization of gerbes. We introduce basic definitions, interpret deformations of a given stack as Maurer-Cartan elements of a differential graded Lie algebra (DGLA), and classify deformations of a given gerbe in terms of Maurer-Cartan elements of the DGLA of Hochschild cochains twisted by the cohomology class of the gerbe. We also classify all deformations of a given gerbe on a symplectic manifold, as well as provide a deformation-theoretic interpretation of the first Rozansky-Witten class.

KW - Deformation

KW - Quantization

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SP - 230

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JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -

Deformation quantization of gerbes

Abstract

Funding

Keywords

ASJC Scopus subject areas

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