本项目主要研究李超代数及其量子化在结构方面和表示方面的若干问题。..结构理论方面：利用Hochschild-Serre谱序列去计算广义正交辛李超代数和广义Periplectic李超代数的高阶同调群，确定其与结合超代数上（斜）二面体同调群之间的关系。..表示理论方面：一方面，利用自由场实现去构造仿射李超代数的权空间有限的最高权表示，并给出它们不可约的充分必要条件。另一方面，我们将建立量子Queer超代数不变量理论中的第一、二基本定理。

In this project, we will focus on some problems on structure theory and representation theory Lie superalgebras and their quantization...On structure theory：We will compute the homology group of generalized ortho-sympletic Lie superalgebras and generalized Peripletic Lie superalgebras by using Hochschild-Serre spectral sequences. Then we will determinate the relationship between the homology groups of these Lie superalgebras and the (skew) dihedral homology groups of associative superalgebras...On representation theory: On one hand, we will use the free fields to construct a family of highest weight representations with finite-dimensional weight spaces for affine Lie superalgebras, and obtain the necessary and sufficient conditions for the representations to be irreducible. On the other hand, we will establish the first and second fundamental theorems of invariant theory for quantum Queer superalgebras.