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引用次数: 0
摘要
本文的目的是描述由一个元素生成的八元子模子的特征，与其他规范划分代数相比，八元子模子非常复杂。为此，我们引入了一种新的特性，阐明了八离子双模子中换元器和关联器之间的关系。值得注意的是，换元可以用关联子的线性组合来表示。这一现象与四元数情况形成了鲜明对比，四元数情况导致了唯一的右八元数标量乘法，在形成八元数双模块的意义上与原始的左八元数模块结构兼容。借助这一特性，我们得到了八离子双模中元素实部和虚部的新表达式。最终，我们得到由一个元素 x 生成的子模块是 \({\mathbb {O}}^5x\) 而不是 \({\mathbb {O}}x\).
The aim of this article is to characterize the octonionic submodules generated by one element, which is very complicated compared with other normed division algebras. To this end, we introduce a novel identity that elucidates the relationship between the commutator and associator within an octonionic bimodule. Remarkably, the commutator can be expressed in terms of the linear combination of associators. This phenomenon starkly contrasts with the quaternionic case, which leads to a unique right octonionic scalar multiplication compatible with the original left octonionic module structure in the sense of forming an octonionic bimodule. With the help of this identity, we get a new expression of the real part and imaginary part of an element in an octonionic bimodule. Ultimately, we obtain that the submodule generated by one element x is \({\mathbb {O}}^5x\) instead of \({\mathbb {O}}x\).
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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