标题： 八元数表示的李群$SL(2,{\mathbb O})$ 显示英文标题

标题： Octonionic presentation for the Lie group $SL(2,{\mathbb O})$

摘要： 本文的目的是提供李群$SL(2,{\mathbb O})$的八元数描述。 主要结果指出，它可以通过从$\mathfrak{h}_2({\mathbb O})$到自身的可逆且行列式保持变换自由生成得到。 给出了$G_2$生成元的一个有趣的特征。 此外，构建了李代数$\mathfrak{sl}(2,{\mathbb K})$对于${\mathbb K}={\mathbb R}, {\mathbb C}, {\mathbb H}, {\mathbb O}$及其相应洛伦兹代数之间的显式同构。 显示英文摘要

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.