Deformation quantization in algebraic geometry

Amnon Yekutieli

doi:10.1016/j.aim.2005.06.009

Deformation quantization in algebraic geometry

Amnon Yekutieli

Department of Mathematics

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

42 Scopus citations

Abstract

We study deformation quantizations of the structure sheaf O_X of a smooth algebraic variety X in characteristic 0. Our main result is that when X is D-affine, any formal Poisson structure on X determines a deformation quantization of O_X (canonically, up to gauge equivalence). This is an algebro-geometric analogue of Kontsevich's celebrated result.

Original language	English
Pages (from-to)	383-432
Number of pages	50
Journal	Advances in Mathematics
Volume	198
Issue number	1 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.aim.2005.06.009
State	Published - 1 Dec 2005

Keywords

DG Lie algebras
Deformation quantization
Formal geometry
Noncommutative algebraic geometry

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2005.06.009

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title = "Deformation quantization in algebraic geometry",

abstract = "We study deformation quantizations of the structure sheaf OX of a smooth algebraic variety X in characteristic 0. Our main result is that when X is D-affine, any formal Poisson structure on X determines a deformation quantization of OX (canonically, up to gauge equivalence). This is an algebro-geometric analogue of Kontsevich's celebrated result.",

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N2 - We study deformation quantizations of the structure sheaf OX of a smooth algebraic variety X in characteristic 0. Our main result is that when X is D-affine, any formal Poisson structure on X determines a deformation quantization of OX (canonically, up to gauge equivalence). This is an algebro-geometric analogue of Kontsevich's celebrated result.

AB - We study deformation quantizations of the structure sheaf OX of a smooth algebraic variety X in characteristic 0. Our main result is that when X is D-affine, any formal Poisson structure on X determines a deformation quantization of OX (canonically, up to gauge equivalence). This is an algebro-geometric analogue of Kontsevich's celebrated result.

KW - DG Lie algebras

KW - Deformation quantization

KW - Formal geometry

KW - Noncommutative algebraic geometry

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U2 - 10.1016/j.aim.2005.06.009

DO - 10.1016/j.aim.2005.06.009

M3 - Article

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SP - 383

EP - 432

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1 SPEC. ISS.

ER -

Deformation quantization in algebraic geometry

Abstract

Keywords

ASJC Scopus subject areas

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