二维Hom-preLie代数的分类

讨论了复数域上的二维Hom-Novikov 代数与Hom-preLie代数的基本性质以及分类。给出了Hom-Novikov 代数与Hom-preLie代数相关的一些基本定义和Hom-preLie是Pre-Lie型的必要条件;讨论Hom-preLie代数的直和,给出了两个Hom-preLie代数之间存在代数同态的充分必要条件。利用这些定义及其简单的性质,完成二维Hom-Novikov 代数与Hom-preLie代数的分类

Classification of Hom-preLie Algebras in Dimension Two

In this paper, we mainly discuss the basic properties and the classification of Hom-Novikov algebras and Hom-preLie algebras in dimension two in the complex field. At first, we give the definition of the Hom-Novikov algebras, Hom-preLie algebras and some related defi-nitions. Then we discuss regular Hom-preLie algebras and give the necessary conditions for an Hom-preLie algebras to be pre-Lie type. We also give the direct sum of Hom-preLie alge-bras and get the necessary and sufficient condition for the existence of homomorphism between two Hom-preLie algebras. At last, with these definitions and their basic properties, we obtain the classification of the Hom-Novikov algebras and Hom-preLie algebras in two dimensions.