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The purpose of this paper is to provide an octonionic description of the Liegroup $SL(2,{\mathbb O})$. The main result states that it can be obtained as afree group generated by invertible and determinant preserving transformationsfrom $\mathfrak{h}_2({\mathbb O})$ onto itself. An interesting characterizationis given for the generators of $G_2$. Also, explicit isomorphisms areconstructed between the Lie algebras $\mathfrak{sl}(2,{\mathbb K})$, for${\mathbb K}={\mathbb R}, {\mathbb C}, {\mathbb H}, {\mathbb O}$, and theircorresponding Lorentz algebras.

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