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arXiv · 0808.4125

Poisson quasi-Nijenhuis structures with background

Paulo Antunes
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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 $(π,ω)$ 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 $π$ and $ω$.

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Paulo Antunes. 2008-08-29. Poisson quasi-Nijenhuis structures with background. https://doi.org/10.1007/s11005-008-0272-5

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