Reduction of Courant algebroids and generalized complex structures

2005/09/30 by Henrique Bursztyn, Gil R. Cavalcanti, Marco Gualtieri · 11 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.DG #math.SG

paper · pdf · doi:10.1016/j.aim.2006.09.008

published as Adv. Math., 211 (2), 2007, 726--765 · 34 pages. Presentation greatly improved, one subsection added, errors corrected, references added. v3: a few changes in the presentation, material slightly reorganized, final version to appear in Adv. in Math

arxiv created 2006/09/20 · openalex publication_date 2006/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We present a theory of reduction for Courant algebroids as well as Dirac structures, generalized complex, and generalized Kähler structures which interpolates between holomorphic reduction of complex manifolds and symplectic reduction. The enhanced symmetry group of a Courant algebroid leads us to define extended actions and a generalized notion of moment map. Key examples of generalized Kähler reduced spaces include new explicit bi-Hermitian metrics on \CC P².

Citations

• Equivariant Cohomology and Gauged Bosonic sigma-Models
• Geometric quantization and multiplicities of group representations
• Reduction of symplectic manifolds with symmetry
• Reduction and submanifolds of generalized complex manifolds
• Generalized Calabi-Yau Manifolds

Cited by

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• Generalized Kähler Potentials from Supergravity
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• Global aspects of T-duality, gauged sigma models and T-folds
• Toric generalized Kähler structures. III
• On homotopy Poisson actions and reduction of symplectic Q-manifolds
• Kaluza-Klein reduction of low-energy effective actions: geometrical approach
• E-Courant Algebroids
• Gauge transformation of double field theory for open string
• Dirac structures of omni-Lie algebroids
• The general (2, 2) gauged sigma model with three-form flux