Split Courant algebroids as $L_{\infty}$-structures

TL;DR

This paper establishes a precise correspondence between split Courant algebroids and multiplicative curved L-infinity algebras, extending to morphisms and twisting operations, thus deepening the algebraic understanding of these geometric structures.

Contribution

It introduces a novel one-to-one correspondence between split Courant algebroids and multiplicative curved L-infinity algebras, including their morphisms and twisting behavior.

Findings

Correspondence between split Courant algebroids and curved L-infinity algebras

Extension of the correspondence to Nijenhuis morphisms

Compatibility with twisting by bivectors

Abstract

We show that split Courant algebroids, i.e., those defined on a Whitney sum $A \oplus A^*$, are in a one-to-one correspondence with multiplicative curved $L_\infty$-algebras. This one-to-one correspondence extends to Nijenhuis morphisms and behaves well under the operation of twisting by a bivector.