Omni-Lie algebroids
Mathematical Physics
2007-10-11 v1 math.MP
Symplectic Geometry
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).
Keywords
Cite
@article{arxiv.0710.1923,
title = {Omni-Lie algebroids},
author = {Z. Chen and Z. -J. Liu},
journal= {arXiv preprint arXiv:0710.1923},
year = {2007}
}
Comments
15 pages, no figure