Tulczyjew triples and higher Poisson/Schouten structures on Lie algebroids

Abstract

We show how to extend the construction of Tulczyjew triples to Lie algebroids via graded manifolds. We also provide a generalisation of triangular Lie bialgebroids as higher Poisson and Schouten structures on Lie algebroids.

28 pages. Completely rewritten and improved. Typos corrected. A version is to appear in Reports on Mathematical Physics, Vol.66, No. 2, 2010. Further minor typos corrected

References in corpus (6)

• Supergroupoids, double structures, and equivariant cohomology
• Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket
• Poisson quasi-Nijenhuis structures with background
• Mackenzie theory and Q-manifolds
• Homotopy Batalin-Vilkovisky algebras
• Graded geometry and Poisson reduction

Cited by in corpus (4)

• From $L_{\infty }$-algebroids to higher Schouten/Poisson structures
• Homological sections of Lie algebroids
• Kirillov structures up to homotopy
• A supergeometric approach to $L_{\infty }$-bialgebras