自同构群是数学研究中的一个重要不变量，其在代数学和几何学中都扮演着十分关键的角色。近年研究表明，非交换代数自同构群与判别式、局部幂零导子、Zariski消去问题、Tits理论、代数同构问题、代数分类问题以及代数同调理论等都有着密切的联系。本项目主要研究内容包括：计算并研究非交换代数的判别式，从而研究代数自同构群问题、Zariski消去问题和Tits理论等，解决代数同构问题和代数分类问题等相关问题；研究群和Hopf代数在非交换代数上的作用，给出作用的分类，计算作用的不变量，研究不变量的同调性质等，从而揭示所研究代数的本质属性；研究非交换代数的导子、局部幂零导子、导子李代数和Makar-Limanov不变量，解决代数的自同构问题和分类问题。本项目旨在通过对非交换代数的判别式、导子、自同构群和不变量的研究，发展非交换代数理论，同时促进非交换代数、同调代数和代数几何等相关领域的发展。

The automorphism group of an algebra is an important invariant in mathematics. It plays a remarkable role in algebra and geometry. There is a close connection between automorphism problems of noncommutative algebra and discriminants, locally nilpotent derivations, Zariski cancellation problems, Tits alternative theories, isomorphisms of algebras, classifications of algebras, homological properties, and so on. In the project, we will investigate discriminants of noncommutative algebras, compute automorphism groups of noncommutative algebras, study the Zariski cancallation problems, Tits alternative theories of noncommutative algebras and so on. We will study and resolve questions which come from isomorphisms and classifications of algebras. The invariant theory of noncommutative algebra will be studied in this project. We will study actions of groups and Hopf algebras on noncommutative algebras, compute invariant subalgebras, find homological properties, then reveal essential attributes of noncommutative algebras. The project will also study derivations, locally nilpotent derivations, Lie algebras generated by locally nilpotent derivations and Makar-Limanov invariants. Then we will study automorphisms and classifications of algebras. Research on discriminants, derivations, automorphism groups and invariants of noncommutative algebras will help the development of noncommutative algebras. It will promote the development of noncommutative algebra, homological algebra, algebraic geometry and other related fields.