具有Z_3-分次结构的线性代数问题  

The Linear algebra problems with Z_3-graded structure

作　　者：毕艳会[1] 李广津 

机构地区：[1]南昌航空大学数学系,江西南昌330063

出　　处：《南昌大学学报（理科版）》2014年第6期537-540,547,共5页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金(11126338;11201218);南昌航空大学博士启动基金(EA201107186)

摘　　要：利用G-分次结构理论,研究具有Z3-分次结构的线性代数问题。首先,得到了Z3-分次向量空间、Z3-分次代数、Z3-分次李代数和Z3-分次子空间的基本概念。其次,给出一种由已知的Z3-分次代数构造左对称的Z3-分次代数的方法,同时提出两种构造Z3-分次李代数的方法。最后,给出Z3-分次子空间的两个基本性质,并利用Z3-分次李代数之间的同态与同构映射,得到了关于Z3-分次李代数的同态与同构定理。从而对G-分次结构理论进行了推广,并得到了相应的结果。Using the theory of Z3-graded structure,we studied the linear algebra problems with Z3-graded structure.The basic definitions of Z3-graded vector space,Z3-graded algebra,-graded Lie algebra and Z3-graded subspace were obtained firstly.Then we gave a method of constructing left-symmetricZ3-graded algebra according to the knownZ3-graded algebra.Meanwhile,two methods of constructing Z3-graded Lie algebra were proposed.Finally,two basic properties of Z3-graded subspace were given.Furthermore,the homomorphism and isomorphism theorems between Z3-graded Lie algebras were obtained as well by using the homomorphism and isomorphism between Z3-graded Lie algebras.We generalized the theory of Z3-graded structure,and reached the relevant conclusions.

关 键 词：Z3-分次向量空间 Z3-分次代数 Z3-分次李代数 Z3-分次子空间 

分 类 号：O151.2[理学—数学]