二维Hom-preLie代数的分类  

Classification of Hom- preLie Algebras in Dimension Two

作　　者：安慧辉[1] 康健[1] 王治淳 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《大连民族学院学报》2014年第5期527-531,共5页Journal of Dalian Nationalities University

摘　　要：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。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.

关 键 词：Hom-Novikov代数 Hom-preLie代数 NOVIKOV代数 

分 类 号：O152.5[理学—数学]