论文标题
八世纪双模块
Octonionic bimodule
论文作者
论文摘要
本文制定了八世纪双模模的结构。事实证明，每个八个离子双模模是张量的产物，八元离子双模模的类别与真实矢量空间的类别同构。我们表明，类似于四元组的八世纪双模型也有一个实际的部分结构。与四元组设置不同，八元双模块的结构是由其左模块结构唯一决定的，因此只能通过左乘法获得实际部分。一个元素产生的八世代间模型的结构更多地涉及，这导致了许多障碍，进一步发展了八世纪功能分析。我们介绍了一个循环分解的概念，以解决这种困难。使用此概念，我们对八元离子模型中一个元素生成的子模块进行了完整的描述。本文清除了$Ø$模型的结构的障碍，用于后来对八元功能分析的研究。
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.
