LA-Courant algebroids and their applications

Abstract

In this thesis we develop the notion of LA-Courant algebroids, the infinitesimal analogue of multiplicative Courant algebroids. Specific applications include the integration of q- Poisson (d, g)-structures, and the reduction of Courant algebroids. We also introduce the notion of pseudo-Dirac structures, (possibly non-Lagrangian) subbundles W \subseteq E of a Courant algebroid such that the Courant bracket endows W naturally with the structure of a Lie algebroid. Specific examples of pseudo-Dirac structures arise in the theory of q-Poisson (d, g)-structures.

arXiv comment137 Pages, 5 figures, phd thesis

References in corpus (22)

• Courant algebroids, derived brackets and even symplectic supermanifolds
• Reduction of Courant algebroids and generalized complex structures
• Higher vector bundles and multi-graded symplectic manifolds
• Semiclassical approximation in Batalin-Vilkovisky formalism
• Some title containing the words "homotopy" and "symplectic", e.g. this one
• Courant Algebroids and Strongly Homotopy Lie Algebras
• Supergroupoids, double structures, and equivariant cohomology
• Symmetries in generalized Kähler geometry
• Hamiltonian symmetries and reduction in generalized geometry
• Quasi-Hamiltonian groupoids and multiplicative Manin pairs
• Double Lie algebroids and the double of a Lie bialgebroid
• Multiplicative Dirac structures on Lie groups
• Q-groupoids and their cohomology
• Mackenzie theory and Q-manifolds
• On homotopy Poisson actions and reduction of symplectic Q-manifolds
• Graded geometry and Poisson reduction
• Universal lifting theorem and quasi-Poisson groupoids
• Q-manifolds and Mackenzie theory: an overview
• Topology of generalized complex quotients
• Moser Lemma in Generalized Complex Geometry
• Dirac structures, nonholonomic systems and reduction
• Singular Reduction of Generalized Complex Manifolds

Cited by in corpus (12)

• Courant Algebroids. A Short History
• Pre-Courant Algebroids
• The Geometrisation of $\mathbb{N}$-manifolds of degree 2
• Dorfman connections and Courant algebroids
• VB-Courant algebroids, E-Courant algebroids and generalized geometry
• Transitive Courant algebroids and double symplectic groupoids
• The Classification of Dirac Homogeneous Spaces
• Categorification of VB-Lie algebroids and VB-Courant algebroids
• Manin triples on multiplicative Courant algebroids
• Linear generalised complex structures
• Deformations of Courant Algebroids and Dirac Structures via Blended Structures
• Pseudo-Dirac Structures