Virasoro代数在无限维李代数领域中占有重要的地位。本项目研究两类与Virasoro代数相关的无限维李代数。其中第一类是一类阶化李代数，这样的一个阶化李代数g同构于有理量子环面上导子李代数的一个子代数，且包含一个高阶Virasoro代数。高阶Virasoro代数在交换环面上导子李代数的权空间有限维不可约模的分类过程中扮演着至关重要的角色，而我们观察到要研究有理量子环面上导子李代数的权空间有限维不可约模时，扮演类似角色的李代数就是阶化李代数g。对李代数g，本项目的研究包括计算其泛中心扩张，构造相应的中间序列模、高低权模，并探讨其权空间有限维不可约模分类的可能性。本项目研究的第二类李代数称为分式Virasoro代数，它的结构较Virasoro代数更复杂，而且生成元算子是非局部的。本项目研究分式Virasoro代数的中间序列模、高低权模，并探讨其权空间有限维不可约模分类的可能性。

The Virasoro algebra plays an important role in the infinite dimensional Lie algebra area. Here we mean to study two classes of Lie algebras related to the Virasoro algebra, one of which is a class of graded Lie algebras. A Lie algebra g in this class is isomorphic to a subalgebra of the algebra of derivations over a rational quantum torus, and contains a higher rank Virasoro subalgebra. When considering the classification of irreducible modules with finite dimensional weight spaces for the algebra D of derivations over a commuting torus, the higher rank Virasoro algebra builds a bridge between the algebra D and the Virasoro algebra. We notice that our Lie algebra g may play a similar part when considering the classification problem for the rational quantum torus case. For this algebra g, we compute its universal central extensions, construct its highest (lowest) weight modules and modules of intermediate series, and furthermore consider the classification of irreducible modules with finite dimensional weight spaces. The second class of Lie algebras we study is called fractional Virasoro algebras. The generating operators of these algebras are nonlocal, different to that of the Virasoro algebra, making the algebra more complex. We study its highest (lowest) weight modules and modules of intermediate series, and furthermore consider the classification of irreducible modules with finite dimensional weight spaces.