Omni-Lie algebroids

Z. Chen; Z. -J. Liu

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arXiv · 0710.1923

Omni-Lie algebroids

Z. Chen·Z. -J. Liu

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Abstract

A generalized Courant algebroid structure is defined on the direct sum bundle D(E) +J(E), where D(E) and J(E) are the gauge Lie algebroid and the jet bundle of a vector bundle E respectively. Such a structure is called an omni-Lie algebroid since it is reduced to the omni-Lie algebra introduced by A.Weinstein if the base manifold is a point. We prove that any Lie algebroid structure on E is characterized by a Dirac structure as the graph of a bundle map from J(E) to D(E).

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Z. Chen, Z. -J. Liu. 2007-10-10. Omni-Lie algebroids. https://arxiv.org/abs/0710.1923

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