Right invariant Poisson Nijenhuis structures on Lie groupoids Correspondence and Classification

Abstract

In this paper, we introduce right-invariant Poisson-Nijenhuis Structures on Lie groupoids and their infinitesimal counterparts as called (Poisson bivector, Nijenhuis operator) structures. Also, we present a one-to-one correspondence between (Poisson bivector, Nijenhuis operator) structures on Lie algebroids with (Poisson, Nijenhuis) structures on their Lie groupoids under certian conditions. Also, we give some illustrative examples .

12 pages, no figures. Uses xy-pic for diagrams. AMS: 53D17, 22A22, 58H05, 53D18, 37K10. Revised and extended version of author's 2020 paper, with complete proofs and new examples