【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。更多还原

【Abstract】 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 Hom-Lie algebra on the Lie algebra gl2( C) is also obtained,from which a complete classification of Hom-Lie algebras on the Lie algebra gl2( C) is presented.更多还原