The 2-graded decompositions of simple Lie algebras g, are classified and the types of subalgebras geV, g0 are determined. The following table is the results of geV, g0 for the exceptional Lie algebras of type E8 (Kaneyuki [2]).In the previous papers [7], [13], we gave group realizations of gev, g0 for the ex ceptional universal linear Lie groups G of type G2, F4, E6 and E7. Now, in this paper, for the exceptional univesal linear Lie groups G of type E8, we realize the subgroups Gev, G0 of G corresponding to gev, go of g = Lie G. Our results are as follows. But as for the results of (E8C)ev, (E8(8))ev and (E8(-24))ev, we refer to [10] (cf. [12]).
The compact simply connected Riemannian 4-symmetric spaces were classified by J. A. Jime ´nez as the type of Lie algebra. Needless to say, these spaces as homogeneous manifolds are of the form G=H, where G is a connected compact simple Lie group with an automorphism g g of oder 4 on G and H is a fixed points subgroup G g of G. In the present article, as Part I, for the connected compact exceptional Lie group E 8 , we give the explicit form of automorphism s s 0 4 of order 4 on E 8 induced by the C-linear transformation s 0 4 of 248-dimensional vector space e C 8 and determine the structure of the group ðE 8 Þ s 0 4 . This amounts to the global realization of one of seven cases with an automorphism of order 4 corresponding to the Lie algebra h ¼ soð6Þ l soð10Þ.
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