Lie brackets on affine bundles
arXiv:math/0203112
Abstract
Natural analogs of Lie brackets on affine bundles are studied, based on natural examples from differential geometry and analytical mechanics. In particular, a close relation to Lie algebroids and, by a sort of duality, to affine analogs of Poisson structures is established as well as affine versions of the complete lift of a section and the Cartan exterior calculus.
22 pages, Lamstex. The revised version, to appear in Annals of Global Analysis and Geometry