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

Decomposition of compact exceptional Lie groups into their maximal tori

“…Here γ, γ ′ ∈ G 2 ⊂ F 4 ⊂ E 6 ⊂ E 7 , σ, σ ′ ∈ F 4 ⊂ E 6 ⊂ E 7 and ι ∈ E 7 . For the cases of the graded Lie algebras g of the second kind and third kind, the corresponding subalgebras g 0 , g ev , g ed of g are realized as the intersection of those fixed point subgroups of the commutative involutive automorphisms ( [3], [6], [7], [10], [11], [12]).…”