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| 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. |
| 关键词: 双线性映射 零积决定的代数 单位积决定的代数 |
| DOI： |
| 分类号:O151.2 |
| 基金项目:Supported by the Fundamental Research Funds for the Central Universities (2010LKSX05);the National Natural Science Foundation of China (11171343). |
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| A CLASS OF IDENTITY PRODUCT DETERMINED JORDAN ALGEBRAS |
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GE Hui,LI Xiao-wei
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| Abstract: |
| 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 M which preserve identity (Jordan) product. |
| Key words: bilinear maps zero product determined algebras identity product determined algebras |
