On quantization functors of Lie bialgebras
type: Item
instance of: scholarly article
title: On quantization functors of Lie bialgebras
zbMATH Open document ID: 1015.17007
DOI: 10.1023/A:1019782906081
author: Benjamin Enriquez
published in: Acta Applicandae Mathematicae
publication date: 2003-03-11T00:00:00Z
review text: This is a survey on recent work on quantization functors of Lie bialgebras. Let QUE be the category of quantized universal enveloping algebras over a field of characteristic 0, and let LBA be the category of Lie bialgebras. The operation of taking the semiclassical limit defines a functor \(\text{SC}:\text{QUE}\rightarrow \text{LBA}\). A quantization functor is a functor \(Q:\text{LBA}\rightarrow \text{QUE}\) such that \(\text{SC}\circ Q\) is isomorphic to the identity. It is shown how the set of quantization functors has a structure of a torsor, and that the Etingof-Kazhdan map [\textit{P. Etingof} and \textit{D. Kazhdan}, Sel. Math., New Ser. 2, 1--41 (1996; Zbl 0863.17008)] is a morphism of torsors. The infinitesimal of this map is computed, and as a consequence it is shown that the quantization functors of finite-dimensional Lie bialgebras are independent of the choice of an associator.
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 17B62
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 1879588
zbMATH Keywords: quantization functor
zbMATH Keywords: Lie bialgebra
zbMATH Keywords: associator
zbMATH Keywords: props
zbMATH Keywords: Grothendieck-Teichmüller Lie algebras
reviewed by: Sorin Dascalescu
MaRDI profile type: Publication
full work available at URL: a:1019782906081
OpenAlex ID: W206736890
description: scientific article; zbMATH DE number 1879588