AV-Courant algebroids and generalized CR structures

Abstract

We construct a generalization of Courant algebroids which are classified by the third cohomology group $H^3(A,V)$, where $A$ is a Lie Algebroid, and $V$ is an $A$-module. We see that both Courant algebroids and ${\mathcal{E}}^1(M)$ structures are examples of them. Finally we introduce generalized CR structures on a manifold, which are a generalization of generalized complex structures, and show that every CR structure and contact structure is an example of a generalized CR structure.

18 pages

References in corpus (2)

• Dirac structures of omni-Lie algebroids
• Omni-Lie algebroids

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