Generalized Complex and Dirac Structures on Homogeneous Spaces

Details Generalized Complex and Dirac Structures on Homogeneous Spaces Generalized Complex and Dirac Structures on Homogeneous Spaces

2007-12-17

arxiv.org/abs/0712.2627v2

Mathematics

Differential Geometry

Preprint

Scientific paper

We partially describe equivariant Dirac and generalized complex structures on a homogeneous space $G/K$ by giving equivalent data involving only the Lie algebra. We consider real semisimple adjoint orbits in any semisimple Lie algebra over $\mathbb R$ and real nilpotent orbits in $sl_n (\mathbb R)$. We give a complete classification for Riemannian symmetric spaces and for a compact group modulo a closed, connected subgroup containing a Cartan subgroup.

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