Lie brackets on affine bundles

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

References in corpus (4)

• Lie algebroids and Poisson-Nijenhuis structures
• Generalized Lie bialgebroids and Jacobi structures
• Algebroids - general differential calculi on vector bundles
• Lie algebroid structures on a class of affine bundles

Cited by in corpus (8)

• Lagrangian submanifolds and dynamics on Lie affgebroids
• Infinitesimal Automorphisms of VB-groupoids and algebroids
• Deformations of Linear Lie Brackets
• The Schroedinger operator as a generalized Laplacian
• Almost Commutative Q-algebras and Derived brackets
• Deformation Cohomology of Lie Algebroids and Morita Equivalence
• Jacobi groupoids and generalized Lie bialgebroids
• On Lie semiheaps and ternary principal bundles