八元数中算子之间的关系及应用-Almansi分解  

Some Relation of Operators and Its Applications to Almansi Decomposition in Octonionic Space

作　　者：李鑫[1] 王海燕[2] 

机构地区：[1]石家庄职业技术学院电气与电子工程系,河北石家庄050081 [2]天津职业技术师范大学理学院,天津300222

出　　处：《数学的实践与认识》2016年第4期277-283,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61272541;11526154);天津职业技术师范大学科研启动基金(KYQD14041)

摘　　要：八元数是四元数的非结合推广,由于其乘法的非结合性质,使得其在YangMills方程、黑洞、弦论中具有重要的应用.给出了八元数中算子之间的一些运算关系,并由此导出Almansi分解定理,实现了Almansi分解定理在非交换非结合空间推广的目的.Octonion is the generalization of quaternion to non-associative space, which has applications in fields such as Yang-Mills equations, black hole and string theory. This paper is devoted to generalize Almansi decomposition theorem into non-commutative and nonassociative space, which is based on some relations of operators in octonionic space.

关 键 词：八元数 非交换非结合空间 Almansi分解定理 

分 类 号：O177[理学—数学]