Note on pre-Courant algebroid structures for parabolic geometries

Abstract

This note aims to demonstrate that every parabolic geometry has a naturally defined per-Courant algebroïd structure. This structure is a Courant algebroïd if and only if the the curvature $\kappa$ of the Cartan connection vanishes. In all other cases, if the parabolic geometry is regular, there does not exist a natural universal expression for a Courant bracket.

A short note on Courant brackets on parabolic geometries. 2nd Version. Removed an erronous proof

Cited by in corpus (7)

• Leibniz 2-algebras and twisted Courant algebroids
• Pre-Courant Algebroids
• Twisted Courant algebroids and coisotropic Cartan geometries
• Cartan Connections on Lie Groupoids and their Integrability
• Courant Algebroids in Parabolic Geometry
• Lie Algebroid Invariants for Subgeometry
• Dirac and Generalized Complex Structures on Cartan Geometries