Poisson quasi-Nijenhuis structures with background

Details Poisson quasi-Nijenhuis structures with background Poisson quasi-Nijenhuis structures with background

2008-08-29

arxiv.org/abs/0808.4125v1

Mathematics

Differential Geometry

11 pages, submitted to Letters in Mathematical Physics

Scientific paper

10.1007/s11005-008-0272-5

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 $\omega$.

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