Quantization of lie bialgebras via the formality of the operad of little disks

Dmitry Tamarkin

doi:10.1007/s00039-007-0591-1

Quantization of lie bialgebras via the formality of the operad of little disks

Dmitry Tamarkin^*

^*Corresponding author for this work

Mathematics

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

10 Scopus citations

Abstract

We give a proof of the Etingof-Kazhdan theorem on quantization of Lie bialgebras based on the formality of the chain operad of little disks and show that the Grothendieck-Teichmüller group acts non-trivially on the corresponding quantization functors.

Original language	English (US)
Pages (from-to)	537-604
Number of pages	68
Journal	Geometric and Functional Analysis
Volume	17
Issue number	2
DOIs	https://doi.org/10.1007/s00039-007-0591-1
State	Published - Jun 2007

Keywords

Drinfeld associator
Etingof-Kazhdan quantization
Gerstenhaber algebra
Hopf algebra
Lie bialgebra
Operad
PROP
Symmetric monoidal category
t-structure

ASJC Scopus subject areas

Analysis
Geometry and Topology

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10.1007/s00039-007-0591-1

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title = "Quantization of lie bialgebras via the formality of the operad of little disks",

abstract = "We give a proof of the Etingof-Kazhdan theorem on quantization of Lie bialgebras based on the formality of the chain operad of little disks and show that the Grothendieck-Teichm{\"u}ller group acts non-trivially on the corresponding quantization functors.",

keywords = "Drinfeld associator, Etingof-Kazhdan quantization, Gerstenhaber algebra, Hopf algebra, Lie bialgebra, Operad, PROP, Symmetric monoidal category, t-structure",

author = "Dmitry Tamarkin",

note = "Funding Information: Keywords and phrases: Lie bialgebra, Hopf algebra, Gerstenhaber algebra, Etingof– Kazhdan quantization, operad, PROP, symmetric monoidal category, t-structure, Drin-feld associator AMS Mathematics Subject Classification: 18D10, 18D50, 18G35 Partially supported by an NSF Grant and A. Sloan Research Fellowship.",

year = "2007",

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doi = "10.1007/s00039-007-0591-1",

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journal = "Geometric and Functional Analysis",

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AU - Tamarkin, Dmitry

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PY - 2007/6

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N2 - We give a proof of the Etingof-Kazhdan theorem on quantization of Lie bialgebras based on the formality of the chain operad of little disks and show that the Grothendieck-Teichmüller group acts non-trivially on the corresponding quantization functors.

AB - We give a proof of the Etingof-Kazhdan theorem on quantization of Lie bialgebras based on the formality of the chain operad of little disks and show that the Grothendieck-Teichmüller group acts non-trivially on the corresponding quantization functors.

KW - Drinfeld associator

KW - Etingof-Kazhdan quantization

KW - Gerstenhaber algebra

KW - Hopf algebra

KW - Lie bialgebra

KW - Operad

KW - PROP

KW - Symmetric monoidal category

KW - t-structure

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SP - 537

EP - 604

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 2

ER -

Quantization of lie bialgebras via the formality of the operad of little disks

Abstract

Keywords

ASJC Scopus subject areas

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