六元数、Zorn矩阵和$\mathbf{e_{7 \frac12}}$
Sextonions, Zorn Matrices, and $\mathbf{e_{7 \frac12}}$
摘要：
利用适当的约束Zorn矩阵，我们提出了一个新的结构的代数的六元数（代数闭域$\mathbb{C}$）。这允许一个明确的建设，在约旦对，非半单李代数$\mathbf{e_{7 \frac12}}$，中间的$\mathbf{e_{7}}$和$\mathbf{e_{8}}$，以及所有李代数发生在六元行和列的扩展弗赖登塔尔幻方。
英文摘要：
By exploiting suitably constrained Zorn matrices, we present a new construction of the algebra of sextonions (over the algebraically closed field $\mathbb{C}$). This allows for an explicit construction, in terms of Jordan pairs, of the non-semisimple Lie algebra $\mathbf{e_{7 \frac12}}$, intermediate between $\mathbf{e_{7}}$ and $\mathbf{e_{8}}$, as well as of all Lie algebras occurring in the sextonionic row and column of the extended Freudenthal Magic Square.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
