由路代数构造的李代数的同构  

The isomorphism of Lie algebras constructed by path algebras

作　　者：叶昌 YE Chang(Faculty of Science,Huzhou Univ.,Huzhou 313000,China)

机构地区：[1]湖州师范学院理学院,浙江湖州313000

出　　处：《高校应用数学学报（A辑）》2024年第1期105-113,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11901195);湖州师范学院校级科研项目(2018XJKJ48)。

摘　　要：通过路代数的乘法可以自然的构造出李代数.首先给出了无定向圈的路代数构造的李代数的中心.然后证明了两个无定向圈的箭图构造的李代数同构,则存在保次的李代数同构.最后给出了两个交替箭图构造的李代数同构的充要条件是它们有相同的顶点数与箭向数.By the means of multiplication of path algebras,Lie algebras are constructed naturally.In this paper,firstly,the center of Lie algebras constructed by acyclic path algebras are given.Then it is proved that there is a degree preserving Lie algebras isomorphism if the isomorphism of Lie algebras constructed by two acyclic quivers exists.Finally,the necessary and sufficient condition for the isomorphism of Lie algebras constructed by two alternating quivers is that they have the same number of vertexes and arrows.

关 键 词：路代数 李代数 同构 交替箭图 

分 类 号：O153.3[理学—数学]