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• W1605634286 abstract "Let $p$ be a Lie subalgebra of a semisimple Lie algebra $g$ and $(G,P)$ be the corresponding pair of connected Lie groups. A Cartan geometry of type $(G,P)$ associates to a smooth manifold $M$ a principal $P$-bundle and a Cartan connection, and a parabolic geometry is a Cartan geometry where $P$ is parabolic. We show that if $P$ is parabolic, the adjoint tractor bundle of a Cartan geometry, which is isomorphic to the Atiyah algebroid of the principal $P$-bundle, admits the structure of a (pre-)Courant algebroid, and we identify the topological obstruction to the bracket being a Courant bracket. For semisimple $G$, the Atiyah algebroid of the principal $P$-bundle associated to the Cartan geometry of $(G,P)$ admits a pre-Courant algebroid structure if and only if $P$ is parabolic." @default.
• W1605634286 created "2016-06-24" @default.
• W1605634286 creator A5005897864 @default.
• W1605634286 creator A5007474265 @default.
• W1605634286 date "2011-12-29" @default.
• W1605634286 modified "2023-09-27" @default.
• W1605634286 title "Courant Algebroids in Parabolic Geometry" @default.
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