4维幂零左对称代数L_(0)的导子和自同构  

The Derivation and Automorphismof 4-dimensional Nilpotent Left Symmetric Algebra L_(0)

作　　者：杨添惠 吴明忠[1] YANG Tian-hui;WU Ming-zhong(School of Mathematics&Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2023年第2期141-145,共5页Journal of China West Normal University(Natural Sciences)

基　　金：四川省教育厅资助科研项目(17AZ0378);西华师范大学博士科研启动基金项目(15E027);西华师范大学英才科研基金项目(17YC392);西华师范大学基本科研业务费项目(17C048)。

摘　　要：利用导子和自同构的定义,对Kim Hyuk提出的一类4维幂零左对称代数L_(0)进行了讨论。通过分析该类代数的结构特点,讨论导子和自同构在一组生成元上的作用,得到了幂零左对称代数L_(0)及其相邻李代数的导子和自同构的结构,发现了L_(0)的导子代数是可解李代数,找到了L_(0)相邻李代数的内自同构的结构。A class of 4-dimensional nilpotent left symmetric algebra L_(0)proposed by Kim Hyuk is discussed by employing the definitions of derivation and automorphism.The structures of derivations and automorphisms of L_(0)and its sub-adjacent Lie algebras are obtained by analyzing the structural characteristics of L_(0)and exploring the functions of derivations and automorphisms on a set of generators.It is found that the derivation algebra of L_(0)is a solvable Lie algebra and the structure of inner automorphism of L_(0)sub-adjacent Lie algebras is obtained.

关 键 词：左对称代数 相邻李代数 导子 自同构 可解 

分 类 号：O152[理学—数学]