E-Courant algebroids

Abstract

In this paper, we introduce the notion of $E$-Courant algebroids, where $E$ is a vector bundle. It is a kind of generalized Courant algebroid and contains Courant algebroids, Courant-Jacobi algebroids and omni-Lie algebroids as its special cases. We explore novel phenomena exhibited by $E$-Courant algebroids and provide many examples. We study the automorphism groups of omni-Lie algebroids and classify the isomorphism classes of exact $E$-Courant algebroids. In addition, we introduce the concepts of $E$-Lie bialgebroids and Manin triples.

29 pages, no figure

References in corpus (5)

• Reduction of Courant algebroids and generalized complex structures
• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Reduction of Generalized Complex Structures
• Poisson Quasi-Nijenhuis Manifolds
• Courant algebroids and Poisson Geometry

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• VB-Courant algebroids, E-Courant algebroids and generalized geometry
• Categorification of VB-Lie algebroids and VB-Courant algebroids