Tulczyjew triples and higher Poisson/Schouten structures on Lie algebroids

TL;DR

This paper extends the Tulczyjew triple framework to Lie algebroids using graded manifolds and introduces higher Poisson and Schouten structures as generalizations of triangular Lie bialgebroids.

Contribution

It provides a novel extension of Tulczyjew triples to Lie algebroids and generalizes triangular Lie bialgebroids through higher Poisson and Schouten structures.

Findings

Extended Tulczyjew triples to Lie algebroids using graded manifolds

Generalized triangular Lie bialgebroids as higher Poisson and Schouten structures

Established a new framework connecting Lie algebroids with advanced geometric structures

Abstract

We show how to extend the construction of Tulczyjew triples to Lie algebroids via graded manifolds. We also provide a generalisation of triangular Lie bialgebroids as higher Poisson and Schouten structures on Lie algebroids.