Reduction of Courant algebroids and generalized complex structures

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 \emph{extended} actions and a generalized notion of moment map. Key examples of generalized Kähler reduced spaces include new explicit bi-Hermitian metrics on $\CC P^2$.

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

References in corpus (10)

• Introduction to sh Lie algebras for physicists
• Instantons, Poisson structures and generalized Kaehler geometry
• Courant Algebroids and Strongly Homotopy Lie Algebras
• Symmetries in generalized Kähler geometry
• Reduction of Generalized Complex Structures
• Hamiltonian symmetries and reduction in generalized geometry
• Equivariant Cohomology and Gauged Bosonic sigma-Models
• Omni-Lie Algebras
• Formal Deformations of Dirac Structures
• Reduction and submanifolds of generalized complex manifolds

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