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arXiv · 1709.08168

Poisson-Nijenhuis groupoids

Apurba Das
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Abstract

We define multiplicative Poisson-Nijenhuis structures on a Lie groupoid which extends the notion of symplectic-Nijenhuis groupoid introduced by Sti\'e23non and Xu. We also introduce a special class of Lie bialgebroid structure on a Lie algebroid $A$, called P-N Lie bialgebroid, which defines a hierarchy of compatible Lie bialgebroid structures on $A$. We show that under some topological assumption on the groupoid, there is a one-to-one correspondence between multiplicative Poisson-Nijenhuis structures on a Lie groupoid and P-N Lie bialgebroid structures on the corresponding Lie algebroid.

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Apurba Das. 2017-09-24. Poisson-Nijenhuis groupoids. https://doi.org/10.1016/s0034-4877(19)30095-3

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