From $L_{\infty}$-algebroids to higher Schouten/Poisson structures

TL;DR

This paper establishes a correspondence between $L_{}$-algebroids, described via Q-manifolds, and higher Schouten and Poisson structures on graded supermanifolds, extending classical Lie algebra and algebroid frameworks.

Contribution

It generalizes the known relations for Lie (super)algebras and Lie algebroids to the setting of $L_{}$-algebroids using higher geometric structures.

Findings

$L_{}$-algebroids can be characterized by higher Schouten/Poisson structures

The work extends classical Lie algebra/algebroid constructions to higher structures

Provides a new geometric perspective on $L_{}$-algebroids

Abstract

We show that $L_{\infty}$-algebroids, understood in terms of Q-manifolds can be described in terms of certain higher Schouten and Poisson structures on graded (super)manifolds. This generalises known constructions for Lie (super)algebras and Lie algebroids.