Generalized complex structures and Lie brackets

2004/12/05 by Marius Crainic, Crainic, Marius · 5 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG) #math-ph #math.DG #math.MP #math.SG

paper · pdf · doi:10.48550/arxiv.math/0412097

15 pages

openalex publication_date 2004/12/05 · arxiv created 2004/12/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Generalized Complex Geometry

Cited by

• Two Categories of Dirac Manifolds
• Generalized almost paracontact structures
• The Symplectization Functor
• Reduction and submanifolds of generalized complex manifolds
• Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids

Related

• Multiplicative Dirac structures
• Lie theory of vector bundles, Poisson geometry and double structures
• Pseudo-Dirac Structures
• LA-Courant algebroids and their applications
• Generalizing Geometry - Algebroids and Sigma Models