李群$SL(2,{\mathbb O})$的八元数表示
Octonionic presentation for the Lie group $SL(2,{\mathbb O})$
摘要：
本文的目的是给出李群$SL(2,{\mathbb O})$的八元数描述。主要结果表明，它可以作为一个自由群生成可逆和行列式保持从$\mathfrak{h}_2({\mathbb O})$到自身的转换。给出了$G_2$的生成元的一个有趣的刻画.此外，显式同构构造之间的李代数$\mathfrak{sl}(2,{\mathbb K})$，为${\mathbb K}={\mathbb R}, {\mathbb C}, {\mathbb H}, {\mathbb O}$，和它们相应的洛伦兹代数。
英文摘要：
The purpose of this paper is to provide an octonionic description of the Lie group $SL(2,{\mathbb O})$. The main result states that it can be obtained as a free group generated by invertible and determinant preserving transformations from $\mathfrak{h}_2({\mathbb O})$ onto itself. An interesting characterization is given for the generators of $G_2$. Also, explicit isomorphisms are constructed between the Lie algebras $\mathfrak{sl}(2,{\mathbb K})$, for ${\mathbb K}={\mathbb R}, {\mathbb C}, {\mathbb H}, {\mathbb O}$, and their corresponding Lorentz algebras.
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。
