Nichols代数与Hopf代数、量子群、李代数有着密切的联系，同时也是共形场理论、微分斜变理论中的重要研究对象, 特别地，Nichols代数在有限维点Hopf代数的分类中发挥重要作用，因此对Nichols代数及相关问题的研究是非常有意义的。本项目研究对角形Nichols代数及其Drinfeld double的结构和表示理论。探索对角形Nichols代数的自同构，并尝试刻画其自同构群，研究一类对角形Nichols代数的bosonizations 的Drinfeld double的中心及表示理论。这些研究对掌握对角型Nichols代数及其Drinfeld double的结构，丰富其理论具有重要意义。

Nichols algebras are closely related to Hopf algebras、 quantum groups、 Lie algebras and conformal field theories, and they are also the imoprtant objects in the theory of covariant differential calculus. Therefore it is meaningful to study Nichols algebras and releated topics. This project focuses on the research of the structure and representations of Nichols algebras of diagonal type and their Drinfeld doubles. We will explore the automorphisms of Nichols algebras of diagonal type, and try to characterize their automorphism groups. Besides, we will study the center and the representations of the Drinfeld doubles of bosonizations of diagonal Nichols algebras. These studies are of great significance to understand the structure and enrich the theory of diagonal Nichols algebras and their Drinfeld doubles.