李pseudo-双代数及其相关代数的构建研究

本课题主要研究李pseudo-双代数及其与之有紧密联系的一些代数的构建。考虑任意的李pseudo-双代数的Drinfeld double理论,利用李pseudo-双代数的Drinfeld double和YBE理论,考虑半单李pseudo-代数的Iwasawa分解问题；给出有限的李pseudo-双代数及其Drinfeld double的量子化；探索如何从无穷小pseudo-双代数切入构建李pseudo-双代数，探寻无穷小pseudo-双代数、dendriform pseudo-代数以及pre-李pseudo-代数相互之间的构造关系,并把得到的关系推进到相应的双模范畴和零化子代数、流代数上。

This project mainly study the construction of Lie pseudo-bialgebras and some other related pseudo-algebras. We consider the Drinfeld double theory of any Lie pseudo-bialgebra. Using the theories of Drinfeld double and YBE, we consider the Iwasawa decomposition of semisimple Lie pseudo-algebra.The quantizations of finite Lie pseudo-bialgebra and its Drinfeld double are established. We explore how to construct a Lie pseudo-bialgebra from an infinitesimal pseudo-bialgebra. The connection among infinitesimal pseudo-bialgebras, dendriform pseudo-algebras and pre-Lie pseudo-algebras is also investigated. Construct the corresponding connection at the level of bimodules、annihilation algebra and current algebra.