Lie代数gl(2,C)上的Hom-Lie代数结构(英文)  

Hom-Lie algebra structures on the Lie algebra gl( 2,C)

作　　者：吴海燕[1] 唐孝敏[2] 生玉秋[2] 

机构地区：[1]黑龙江财经学院基础部,哈尔滨150025 [2]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2014年第2期181-184,共4页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Natural Science Foundation of China(11171294);the Natural Science Foundation of Heilongjiang Province(A201013)

摘　　要：研究李代数的同构条件以实现其完全分类。基于复数域上对称矩阵的正交相似分类,利用正交矩阵、伴随矩阵的性质和矩阵计算的技巧,给出Hom-Lie代数同构的条件,得到Lie代数gl2(C)上Hom-Lie代数的同构条件及其同构意义下的一个完全分类。Isomorphism conditions of Lie algebra are studied to achieve the complete classification. Based on the orthogonal similar classification of complex symmetric matrices, an isomorphism condition of Hom-Lie algebra is given by employing some properties of adjoint and orthogonal matrices and using skills of matrix calculation. An isomorphism condition of Horn-Lie algebra on the Lie algebra gl2 （C） is also obtained, from which a complete classification of Horn-Lie algebras on the Lie algebra gl2 （C） is presented.

关 键 词：LIE代数 Hom—Lie代数 对称阵 

分 类 号：O152.55[理学—数学]