八元离子双模
Octonionic bimodule
摘要：
本文给出了八元离子双模的结构。证明了每一个八元数双模都是一个张量积，八元数双模范畴同构于实向量空间范畴。我们证明了八元数双模也存在类似于四元数双模的实部结构。与四元数设置不同，八元数双模结构由其左模结构唯一确定，因此其实部只需左乘即可求出.单元素生成的八元子模的结构涉及较多，这给八元泛函分析的进一步发展带来了许多障碍。我们引入循环分解的概念来处理这个困难。利用这一概念，我们给出了八元双模中由一个元素生成的子模的完整刻画。为以后研究八元泛函分析扫清了$Ø$ -模的结构障碍。
英文摘要：
The structure of octonionic bimodules is formulated in this paper. It turns out that every octonionic bimodule is a tensor product, the category of octonionic bimodules is isomorphic to the category of real vector spaces. We show that there is also a real part structure on octonionic bimodules similar to the quaternion case. Different from the quaternion setting , the octonionic bimodule sturcture is uniquely determined by its left module structure and hence the real part can be obtained only by left multiplication. The structure of octonionic submodules generated by one element is more involved, which leads to many obstacles to further development of the octonionic functional analysis. We introduce a notion of cyclic decomposition to deal with this difficulty. Using this concept, we give a complete description of the submodule generated by one element in octonionic bimodules. This paper clears the barrier of the structure of $Ø$-modules for the later study of octonionic functional analysis.
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