Abstract
A generalized Courant algebroid structure is defined on the direct sum bundle D E ⊕ J E , where D E and J E are, respectively, the gauge Lie algebroid and the jet bundle of a vector bundle E . 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 there is a one-to-one correspondence between Dirac structures coming from bundle maps J E → D E and Lie algebroid (local Lie algebra) structures on E when rank ( E ) ≥ 2 ( E is a line bundle).
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