Nijenhuis forms on $L_\infty$-algebras and Poisson geometry

TL;DR

This paper explores Nijenhuis deformations within $L_$-algebras, unifying various geometric and algebraic structures, and introduces new examples related to higher algebraic and geometric frameworks.

Contribution

It generalizes Nijenhuis deformations to $L_$-algebras, encompassing multiple structures like Lie algebras, Poisson, and Courant structures, and provides new examples linked to higher structures.

Findings

Unified framework for Nijenhuis deformations across multiple structures

Introduction of examples related to Lie n-algebras and n-plectic manifolds

Enhanced understanding of deformation theory in higher algebraic contexts

Abstract

We investigate Nijenhuis deformations of $L_\infty$-algebras, a notion that unifies several Nijenhuis deformations, namely those of Lie algebras, Lie algebroids, Poisson structures and Courant structures. Additional examples, linked to Lie $n$-algebras and $n$-plectic manifolds, are included.