单位积决定的若当矩阵代数(英文)  

A CLASS OF IDENTITY PRODUCT DETERMINED JORDAN ALGEBRAS

作　　者：葛徽[1] 李小微[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221116

出　　处：《数学杂志》2014年第1期25-30,共6页Journal of Mathematics

基　　金：Supported by the Fundamental Research Funds for the Central Universities(2010LKSX05);the National Natural Science Foundation of China(11171343)

摘　　要：本文研究了单位积决定的若当矩阵代数M=Mn(R)的条件及分类问题.利用基矩阵及巧妙对对称双线性映射{·,·}进行构造和扩充,用初等矩阵的方法,获得了一系列新的同样重要的定义,结论与证明(与参考文献[1]相比较),推广了参考文献[1]的结论,作为其应用可以进一步证明了Mn(R)上的任意可逆线性映射都是保单位积的.In this paper, we investigate the condition and classification of the identity product determined Jordan matrix algebras M = Mn（R）. Using the base matrix and the symmetric bilinear map {.,.} skillfully constructed for this purpose and expansion, only elementary matrix method is used. Comparing to the reference [1], we obtain a new series of equally important definition, conclusions and proof improving the conclusions of the reference [1]. As an application we characterize the invertible linear maps on A/I which preserve identity （Jordan） product.

关 键 词：双线性映射 零积决定的代数 单位积决定的代数 

分 类 号：O151.2[理学—数学]