Lie brackets on affine bundles

Janusz Grabowski Institute of Mathematics Polish Academy of Scientes

Katarzyna Grabowska Institute of Mathematics Polish Academy of Scientes

Pawel Urbanski Institute of Mathematics Polish Academy of Scientes

Natural analogs of Lie brackets on affine bundles are studied. In particular, a close relation to Lie algebroids and duality with certain affine analog of Poisson structures is established as well as affine versions of the complete lift and the Cartan exterior calculus.