# Contact Courant algebroids and $L_\infty$-algebras

## TL;DR

This paper constructs $L_infty$-algebras from contact Courant algebroids and isotropic involutive subbundles, extending the work on Courant algebroids to the contact setting and establishing relations between these algebraic structures.

## Contribution

It introduces a novel association of $L_infty$-algebras to contact Courant algebroids and isotropic involutive subbundles, expanding the algebraic framework in contact geometry.

## Key findings

- Constructed $L_infty$-algebra from contact Courant algebroids.
- Associated $p$-term $L_infty$-algebras to isotropic involutive subbundles.
- Established a morphism relating these $L_infty$-algebras in special cases.

## Abstract

Let $L$ be a line bundle over $M$. In this paper we associate an $L_\infty$-algebra to any $L$-Courant algebroid (contact Courant algebroid in the sense of Grabowski). This construction is similar to the work of Roytenberg and Weinstein for Courant algebroids. Next we associate a $p$-term $L_\infty$-algebra to any isotropic involutive subbundle of $(\mathbb{D}L)^p := DL \oplus (\wedge^p (DL)^* \otimes L)$, where $DL$ is the gauge algebroid of $L$. In a particular case, we relate these $L_\infty$-algebras by a suitable morphism.