English

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

R2 v1 2026-06-21T09:29:29.549Z