Poisson quasi-Nijenhuis structures with background

Abstract

We define the Poisson quasi-Nijenhuis structures with background on Lie algebroids and we prove that to any generalized complex structure on a Courant algebroid which is the double of a Lie algebroid is associated such a structure. We prove that any Lie algebroid with a Poisson quasi-Nijenhuis structure with background constitutes, with its dual, a quasi-Lie bialgebroid. We also prove that any pair $(\pi ,\omega )$ of a Poisson bivector and a 2-form induces a Poisson quasi-Nijenhuis structure with background and we observe that particular cases correspond to already known compatibilities between $\pi$ and $\omega$.

11 pages, submitted to Letters in Mathematical Physics

References in corpus (7)

• Courant algebroids, derived brackets and even symplectic supermanifolds
• Lie algebroids and Poisson-Nijenhuis structures
• Poisson Quasi-Nijenhuis Manifolds
• Generalized complex structures and Lie brackets
• Courant algebroid and Lie bialgebroid contractions
• The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction
• On Poisson quasi-Nijenhuis Lie algebroids

Cited by in corpus (8)

• Tulczyjew triples and higher Poisson/Schouten structures on Lie algebroids
• Nijenhuis and Compatible Tensors on Lie and Courant algebroids
• On Jacobi quasi-Nijenhuis algebroids and Courant-Jacobi algebroid morphisms
• Jacobi quasi-Nijenhuis Algebroids
• Compatible structures on Lie algebroids and Monge-Ampère operators
• Reduction and construction of Poisson quasi-Nijenhuis manifolds with background
• Quasi-Lie bialgebroids, Dirac structures and deformations of Poisson quasi-Nijenhuis manifolds
• Nijenhuis structures on Courant algebroids