Tangent and cotangent lifts and graded Lie algebras associated with Lie algebroids

Abstract

Generalized Schouten, Froelicher-Nijenhuis and Froelicher-Richardson brackets are defined for an arbitrary Lie algebroid. Tangent and cotangent lifts of Lie algebroids are introduced and discussed and the behaviour of the related graded Lie brackets under these lifts is studied. In the case of the canonical Lie algebroid on the tangent bundle, a new common generalization of the Froelicher-Nijenhuis and the symmetric Schouten brackets, as well as embeddings of the Nijenhuis-Richardson and the Froelicher-Nijenhuis bracket into the Schouten bracket, are obtained.

LamsTex 1991, 28 pages, to appear in Annals of global analysis and geometry

References in corpus (1)

• Tangent Lifts of Poisson and Related Structures

Cited by in corpus (6)

• Derived brackets
• Lie algebroids and Poisson-Nijenhuis structures
• Algebroids - general differential calculi on vector bundles
• Lagrangian submanifolds and dynamics on Lie affgebroids
• Deformation Quantization of Poisson Structures Associated to Lie Algebroids
• On a geometric framework for Lagrangian supermechanics