On Quantizable Odd Lie Bialgebras

Anton Khoroshkin; Sergei Merkulov; Thomas Willwacher

doi:10.1007/s11005-016-0873-3

On Quantizable Odd Lie Bialgebras

Anton Khoroshkin, Sergei Merkulov, Thomas Willwacher

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

Abstract

Motivated by the obstruction to the deformation quantization of Poisson structures in infinite dimensions, we introduce the notion of a quantizable odd Lie bialgebra. The main result of the paper is a construction of the highly non-trivial minimal resolution of the properad governing such Lie bialgebras, and its link with the theory of so-called quantizable Poisson structures.

Original language	English
Pages (from-to)	1199-1215
Number of pages	17
Journal	Letters in Mathematical Physics
Volume	106
Issue number	9
DOIs	https://doi.org/10.1007/s11005-016-0873-3
State	Published - 1 Sep 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media Dordrecht.

Keywords

Lie bialgebras
Poisson structures
deformation quantization
properads and props

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s11005-016-0873-3

Cite this

@article{d6980a5f3d7740bcb9923d99422a6fbf,

title = "On Quantizable Odd Lie Bialgebras",

abstract = "Motivated by the obstruction to the deformation quantization of Poisson structures in infinite dimensions, we introduce the notion of a quantizable odd Lie bialgebra. The main result of the paper is a construction of the highly non-trivial minimal resolution of the properad governing such Lie bialgebras, and its link with the theory of so-called quantizable Poisson structures.",

keywords = "Lie bialgebras, Poisson structures, deformation quantization, properads and props",

author = "Anton Khoroshkin and Sergei Merkulov and Thomas Willwacher",

note = "Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media Dordrecht.",

year = "2016",

month = sep,

day = "1",

doi = "10.1007/s11005-016-0873-3",

language = "English",

volume = "106",

pages = "1199--1215",

journal = "Letters in Mathematical Physics",

issn = "0377-9017",

publisher = "Springer Netherlands",

number = "9",

}

TY - JOUR

T1 - On Quantizable Odd Lie Bialgebras

AU - Khoroshkin, Anton

AU - Merkulov, Sergei

AU - Willwacher, Thomas

PY - 2016/9/1

Y1 - 2016/9/1

N2 - Motivated by the obstruction to the deformation quantization of Poisson structures in infinite dimensions, we introduce the notion of a quantizable odd Lie bialgebra. The main result of the paper is a construction of the highly non-trivial minimal resolution of the properad governing such Lie bialgebras, and its link with the theory of so-called quantizable Poisson structures.

AB - Motivated by the obstruction to the deformation quantization of Poisson structures in infinite dimensions, we introduce the notion of a quantizable odd Lie bialgebra. The main result of the paper is a construction of the highly non-trivial minimal resolution of the properad governing such Lie bialgebras, and its link with the theory of so-called quantizable Poisson structures.

KW - Lie bialgebras

KW - Poisson structures

KW - deformation quantization

KW - properads and props

UR - http://www.scopus.com/inward/record.url?scp=84978707070&partnerID=8YFLogxK

U2 - 10.1007/s11005-016-0873-3

DO - 10.1007/s11005-016-0873-3

M3 - Article

AN - SCOPUS:84978707070

SN - 0377-9017

VL - 106

SP - 1199

EP - 1215

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 9

ER -

On Quantizable Odd Lie Bialgebras

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this