本项目将研究几类重要的量子代数的表示和实现。研究主要集中在：系统完整的研究量子代数的Drinfeld实现的余积及Hopf代数结构，从而推广现有的Drinfeld同构定理，得到量子仿射代数的Hopf代数同构性质；还将第一次完整研究量子Toroidal代数的余积和Hopf代数结构；同时还将对双参数量子环面代数的结构和表示理论进行研究，最后刻画出单位根情形下的双参数量子代数的有限维表示。本项目的研究内容是当前该领域中非常有意义和具有挑战性的研究课题。这些研究成果将直接丰富量子代数的理论，使得量子代数的结构和表示理论更加完善和成熟，也促进量子代数其它相关问题的研究。

This project will study the realizations and the representations theory of a few kinds of important quantum algebras. The research mainly focuses on the following parts: studying systemly the coproduct and Hopf structures of Drinfeld realization of quantum algebras, and then generalize the and the finite dimensional representation theory of the twisted quantum affine algebras systemically, the second one is the geometric apporach to twisted quantum affine algebras, the third one is the structures and representation theory of two-parameter quantum toroidal algebras as well as describing the finite dimensional representations theory at roots of unity finally. These contents are the challenging problems which are needed to be solved urgently in this research field. The results of the project could greatly enrich the content of the theory of quantum algebra, and make the theory of quantum algebra more complete and mature. At the same time,it could promote the research of other related topics on quantum algebra.