3-graded decompositions of exceptional Lie algebras g and group realizations of gev, g0 and ged, III: G=E8

Abstract

In the articles [4] and [7], we completed the determination of group realizations ${\mathfrak{g}}_{ev}$ and ${\mathfrak{g}}_0$ of $2$-graded decompositions $\mathfrak{g}={\mathfrak{g}}_{-2}\oplus {\mathfrak{g}}_{-1}\oplus {\mathfrak{g}}_0\oplus {\mathfrak{g}}_1\oplus {\mathfrak{g}}_2$ of exceptional Lie algebras $\mathfrak{g}$ for the universal exceptional Lie groups. In the present article, which is a continuation of [5] and [8], we determine group realizations of subalgebras ${\mathfrak{g}}_{ev}$, ${\mathfrak{g}}_0$ and ${\mathfrak{g}}_{ed}$ of $3$-graded decompositions of exceptional Lie algebras $\mathfrak{g}$ for the universal exceptional Lie groups of type $E_8$.