The Pontryagin Class for Pre-Courant Algebroids

Abstract

In this paper, we show that the Jacobiator $J$ of a pre-Courant algebroid is closed naturally. The corresponding equivalence class $[J^{♭}]$ is defined as the Pontryagin class, which is the obstruction of a pre-Courant algebroid to be deformed into a Courant algebroid. We construct a Leibniz 2-algebra and a Lie 2-algebra associated to a pre-Courant algebroid and prove that these algebraic structures are isomorphic under deformations. Finally, we introduce the twisted action of a Lie algebra on a manifold to give more examples of pre-Courant algebroids, which include the Cartan geometry.

26 pages

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Cited by in corpus (10)

• Double Field Theory and Membrane Sigma-Models
• Pre-Courant Algebroids
• Heterotic Reduction of Courant Algebroid Connections and Einstein-Hilbert Actions
• Twisted Courant algebroids and coisotropic Cartan geometries
• Almost Lie Algebroids and Characteristic Classes
• Kaluza-Klein Reduction of Low-Energy Effective Actions: Geometrical Approach
• Geometric BV for twisted Courant sigma models and the BRST power finesse
• The Algebroid Structure of Double Field Theory
• Cohomology for almost Lie algebroids
• Instances of Higher Geometry in Field Theory