Generalized complex structures and Lie brackets
arXiv:math/0412097
Abstract
We look at generalized complex structures from the point of view of Poisson and Dirac geometry and we remark that the puzzling equations underlying the notion of generalized complex structure have miraculously simple meaning when passing to Lie algebroids/groupoids.
15 pages
Cited by in corpus (17)
- Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids
- Symmetries in generalized Kähler geometry
- Reduction of Generalized Complex Structures
- Blow-up of generalized complex 4-manifolds
- Generalizing Geometry - Algebroids and Sigma Models
- Poisson quasi-Nijenhuis structures with background
- Reduction of twisted generalized Kähler structure
- Monge-Ampere equations and generalized complex geometry. The two-dimensional case
- The Symplectization Functor
- Conformal changes of generalized complex structures
- Glanon groupoids
- Reduction and submanifolds of generalized complex manifolds
- Compatible structures on Lie algebroids and Monge-Ampère operators
- Two Categories of Dirac Manifolds
- 2D and 3D topological field theories for generalized complex geometry
- From generalized Kaehler to generalized Sasakian structures
- Integrable geometries and Monge-Ampere equations