Omni-Lie algebroids

Details Omni-Lie algebroids Omni-Lie algebroids

2007-10-10

arxiv.org/abs/0710.1923v1

Physics

Mathematical Physics

15 pages, no figure

Scientific paper

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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