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Jian-yi Shi (1987)
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J. Humphreys (1990)
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Shôshichi Kobayashi, K. Nomizu (1963)
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Garth Warner (1972)
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This paper considers invariant (1, 2)-symplectic almost Hermitian structures on the maximal flag manifod associated to a complex semi-simple Lie group G. The concept of cone-free invariant almost complex structure is introduced. It involves the rank-three subgroups of G, and generalizes the cone-free property for tournaments related to 𝕊l (n,ℂ) case. It is proved that the cone-free property is necessary for an invariant almost-complex structure to take part in an invariant (1, 2)-symplectic almost Hermitian structure. It is also sufficient if the Lie group is not B l , l ≥ 3, G 2 or F 4. For B l and F 4 a close condition turns out to be sufficient.
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Apr 1, 2002
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