论文标题
在类似八位的联想部代数
On the Octonion-like Associative Division Algebra
论文作者
论文摘要
使用基本线性代数，本文阐明并证明了有关最近引入的八元式联想师代数的一些概念。这个类似八元的代数实际上与拆分 - 博物产物代数相同，这是Clifford algebra cl的均匀代数，Clifford algebra cl（4,0）。对于本文中描述的两个半词，显示出八元的代数是一个符号的代数。非零。还提出了关于八度数字的归一化和一些相关结果的其他结果。本文中使用的基本线性代数描述还允许直接的软件实现类似Octonion的代数。
Using elementary linear algebra, this paper clarifies and proves some concepts about a recently introduced octonion-like associative division algebra over R. This octonion-like algebra is actually the same as the split-biquaternion algebra, an even subalgebra of Clifford algebra Cl(4,0). For two seminorms described in the paper, it is shown that the octonion-like algebra is a seminormed composition algebra over R. Moreover, additional results related to the computation of inverse numbers in the octonion-like algebra are introduced, showing that the octonion-like algebra is a seminormed division algebra over R, i.e., division by any number is possible as long as the two seminorms are non-zero. Additional results on normalization of octonion-like numbers and some involutions are also presented. The elementary linear algebra descriptions used in the paper also allow straightforward software implementations of the octonion-like algebra.
