通过形变到拟经典极限的泊松双代数
Poisson bialgebras by deformations-to-quasiclassical limits
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中文总结 AI 辅助
本文将泊松代数的形变-拟经典极限过程推广到双代数层面，推导了泊松双代数的对应关系并通过相干导子阐释，是李双代数量子化过程的无穷小版本。
中文摘要 AI 辅助
泊松代数是交换结合代数的结合代数形变的拟经典极限，本文将这一过程推广到双代数层面。我们推导了泊松双代数，其为交换余交换反对称无穷小双代数的反对称无穷小双代数形变的拟经典极限，可视为霍普夫代数框架下李双代数量子化过程的“无穷小”版本。泊松双代数的此类形变-拟经典极限过程，可等价地通过引入的结合代数匹配对形变及结合代数标准曼宁三元组概念表征，对应拟经典极限分别为泊松代数匹配对与泊松代数标准曼宁三元组，我们通过相干导子阐释这些等价的形变-拟经典极限过程。
英文摘要
Poisson algebras are the quasiclassical limits of associative algebra deformations of commutative associative algebras. This paper extends this process to the level of bialgebras. We derive Poisson bialgebras as the quasiclassical limits of antisymmetric infinitesimal bialgebra deformations of commutative and cocommutative antisymmetric infinitesimal bialgebras. It might be regarded as the ``infinitesimal" version of the quantization process of Lie bialgebras in terms of Hopf algebras. Such deformations-quasiclassical limits process for a Poisson bialgebra is equivalently characterized in terms of the introduced notions of deformations of a matched pair of associative algebras as well as a standard Manin triple of associative algebras, whose corresponding quasiclassical limits are a matched pair of Poisson algebras and a standard Manin triple of Poisson algebras, respectively. We illustrate these equivalent deformations-quasiclassical limits processes via coherent derivations.
发表机构
- Hunan Institute of Science and Technology（湖南理工学院）
- Nankai University（南开大学）
机构由 AI 辅助整理，请以论文原文为准。
