致力于利用有限维代数的表示理论中Ringel-Hall 代数来实现已有的非Kac-Mood代数或构造新的李代数，并在代数表示论与李代数之间的已有联系的基础上应用表示论中范畴的协变化和自等价来研究对应李代数的结构。主要目标有：(1)利用根范畴的Ringel-Hall李代数实现Am, Dn(n>4)型单边椭圆李代数或椭圆根系;(2)利用有限维代数的表示理论实现由小余秩的单位二次型定义的BKL李代数,并在此基础上给出BKL李代数的根系与整基；(3)用非遗传代数的2-循环投射复形的Bridgeland-Hall代数构造新李代数; (4)利用根范畴的协变化范畴构造Kac- Moody代数或四类单边型椭圆李代数的扩张; (5)利用根范畴的自等价,构造对应Kac-Moody代数或四类单边型椭圆李代数的自同构群或Weyl群中的一些特殊元，并通过这些元研究自同构群和Weyl群的结构。

It aims to realize some known non-Kac-Moody algebras or construct new Lie algebras via the representation theory of finite dimensional algebras. Moreover, basing on known relationships between Lie algebras and representation theory of finite dimensional algebras, we study structures of corresponding Lie algebras through equivariantizations and autoequivalences of categories. Main targets are as follows..(1) We will realize simply-laced elliptic Lie algebras or elliptic root systems of type Am, Dn (n>4) via the Ringel-Hall Lie algebras of root categories..(2) We will realize some BKL Lie algebras defined by unit quadratic forms of small corank via the representation theory of finite dimensional algebras. Furthermore， root systems and integral basis of the BKL Lie algebras will be obtained..(3) We will construct new Lie algebrs via Bridgeland-Hall algebras of 2-cyclic complexes of projective modules over non-hereditary algebras..(4) We will construct extensions of Kac-Moody algebras or four simply-laced elliptic Lie algebras via equivariantizations of root categories in the representation theory of finite dimensional algebras..(5)By autoequivalences of root categories, we will construct some special elements in the automorphism groups or Weyl groups of the corresponding Kac-Moody algebras or four simply-laced elliptic Lie algebras. Furthermore, the structures of these groups will be studied through the above special elements.