Lie brackets on affine bundles
  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. 
Janusz Grabowski, Katarzyna Grabowska, Pawel Urbanski