Poisson-Nijenhuis groupoids

Abstract

We define multiplicative Poisson-Nijenhuis structures on a Lie groupoid which extends the notion of symplectic-Nijenhuis groupoid introduced by Stié23non 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.

23 pages

References in corpus (4)

• Tangent Lifts of Poisson and Related Structures
• Poisson Quasi-Nijenhuis Manifolds
• Lie groupoids and the Frolicher-Nijenhuis bracket
• Glanon groupoids

Cited by in corpus (2)

• Cohomology and deformations of compatible Hom-Lie algebras
• Integrating Nijenhuis Structures