Quantization of coboundary Lie bialgebras

• 成果类型: Article
• 署名作者: Enriquez, Benjamin; Halbout, Gilles
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.171.1267
• 发表日期: 2010
• 页码: 1267-1345
• 关键词: algebras

摘要

We show that any coboundary Lie bialgebra can be quantized. For this, we prove that Etingof-Kazhdan quantization functors are compatible with Lie bialgebra twists, and if such a quantization functor corresponds to an even associator, then it is also compatible with the operation of taking coopposites. We also use the relation between the Etingof-Kazhdan construction of quantization functors and the alternative approach to this problem, which was established in a previous work. Let k be a field of characteristic 0. Unless specified otherwise, algebra, vector space, etc., means algebra over k, etc.