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|Title:||Invariant generalized complex structures on flag manifolds|
San Martin, L.A.B.
|Abstract:||Let G be a complex semi-simple Lie group and form its maximal flag manifold F=G∕P=U∕T where P is a minimal parabolic subgroup, U a compact real form and T=U∩P a maximal torus of U. The aim of this paper is to study invariant generalized complex structures on F. We describe the invariant generalized almost complex structures on F and classify which one is integrable. The problem reduces to the study of invariant 4-dimensional generalized almost complex structures restricted to each root space, and for integrability we analyze the Nijenhuis operator for a triple of roots such that its sum is zero. We also conducted a study about twisted generalized complex structures. We define a new bracket ‘twisted’ by a closed 3-form Ω and also define the Nijenhuis operator twisted by Ω. We classify the Ω-integrable generalized complex structure|
|Subject:||Lie, Grupos de|
|Appears in Collections:||IMECC - Artigos e Outros Documentos|
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