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A rank-three condition for invariant (1, 2)-symplectic almost Hermitian structures on flag manifolds

A rank-three condition for invariant (1, 2)-symplectic almost Hermitian structures on flag manifolds 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

A rank-three condition for invariant (1, 2)-symplectic almost Hermitian structures on flag manifolds

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References (9)

Publisher
Springer Journals
Copyright
Copyright © 2002 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s005740200002
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Apr 1, 2002

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