论文标题
Hopf-Galois代数及其泊松结构
Hopf-Galois algebras and their Poisson structures
论文作者
论文摘要
众所周知，HOPF-GALOIS对象具有分析凸起的HOPF代数的张量和分类问题的张量类别的重要研究价值，并且是具有Galois理论风味的Hopf代数的自然概括。在本文中，我们主要证明了Hopf-Galois代数的矿石扩展为HOPF-GALOIS代数的标准，并介绍了Poisson Hopf-Galois代数的概念，并建立Poisson Hopf-Galois代数代数和Poisson hopf hopf algebras之间的关系。此外，我们研究有关泊松多项式代数的Poisson Hopf-galois结构，并主要为Poisson Hopf-Galois代数的泊松包膜代数提供必要和足够的条件，使其成为Hopf-Galois代数。
As is known to all, Hopf-Galois objects have a significant research value for analyzing tensor categories of comodules and classification questions of pointed Hopf algebras, and are natural generalizations of Hopf algebras with a Galois-theoretic flavour. In this paper, we mainly prove a criterion for an Ore extension of a Hopf-Galois algebra to be a Hopf-Galois algebra, and introduce the conception of Poisson Hopf-Galois algebras, and establish the relationship between Poisson Hopf-Galois algebras and Poisson Hopf algebras. Moreover, we study Poisson Hopf-Galois structures on Poisson polynomial algebras, and mainly give a necessary and sufficient condition for the Poisson enveloping algebra of a Poisson Hopf-Galois algebra to be a Hopf-Galois algebra.
