Research On Some Problems Of Hom - Li Chao Algebra

Hom-superalgebra is a kind of Lie algebra deformation. In recent years, HomLie superalgebra has been get more extensive attention and research by algebra scholars. Scholars have been made some progress in the representations theory and the structure theory of Hom-Lie superalgebra. In this paper we mainly studies the four kinds of the typical affine Lie superalgebra of Hom-structure.First of all, in the introduction we introduces the purpose and significance of the thesis, the research status and development trend at home and abroad, the relevant concepts, and the preparation work for the Hom-structure of affine Lie superalgebra.Secondly, we studied the Hom-structure of four types affine Lie superalgebra,and find the map which meet the conditions, and Lie superalgebra is the sufficient and necessary condition of Hom-Lie superalgebra.Finally, we give two examples of Lie superalgebra Hom-module for later study of the Hom-module.