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 (3)

• Poisson Quasi-Nijenhuis Manifolds
• Generalized complex structures and Lie brackets
• On Poisson quasi-Nijenhuis Lie algebroids