论文标题
实际组成代数的基本衍生
Elementary Derivations of the Real Composition Algebras
论文作者
论文摘要
已故的加迪·莫兰（Gadi Moran）的最后一篇论文``重新审视了真正的规范代数'，试图重建发现复数，四元和五十五元的发现以及其性质的证明，仅使用19世纪的数学家所知。在他的研究中，加迪仅使用高中几何形状的欧几里得空间和工具的几何形状的基本特性发现了上述古典结果的简单优雅证明。他的重建强调了欧几里得几何形状与这些代数之间的有趣联系，并避免了这些结果先前推导的先进机械。本文的目的是以众多读者可以访问的方式介绍Gadi的派生。
``Real Normed Algebras Revisited,'' the last paper of the late Gadi Moran, attempts to reconstruct the discovery of the complex numbers, the quaternions and the octonions, as well as proofs of their properties, using only what was known to 19th century mathematicians. In his research, Gadi had discovered simple and elegant proofs of the above-mentioned classical results using only basic properties of the geometry of Euclidean spaces and tools from high school geometry. His reconstructions underline an interesting connection between Euclidean geometry and these algebras, and avoid the advanced machinery used in previous derivations of these results. The goal of this article is to present Gadi's derivations in a way that is accessible to a wide audience of readers.
