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Lie brackets on affine bundles

Janusz Grabowski·Katarzyna Grabowska·Pawel Urbanski
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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.

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Janusz Grabowski, Katarzyna Grabowska, Pawel Urbanski. 2003-03-19. Lie brackets on affine bundles. https://arxiv.org/abs/math/0203112

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