# On the (3,N) Maurer-Cartan equation

## TL;DR

This paper explores the (3,N) Maurer-Cartan equation governing deformations in 3-differential graded algebras, providing explicit formulas, new geometric examples, and applications to N Lie algebroids.

## Contribution

It introduces explicit formulas for the (3,N) Maurer-Cartan equation and new geometric examples of N-differential graded algebras, advancing the understanding of their structure and deformations.

## Key findings

- Derived explicit coefficient formulas for the (3,N) Maurer-Cartan equation.
- Constructed new geometric examples of N-differential graded algebras.
- Applied results to study N Lie algebroids.

## Abstract

Deformations of the 3-differential of 3-differential graded algebras are controlled by the (3,N) Maurer-Cartan equation. We find explicit formulae for the coefficients appearing in that equation, introduce new geometric examples of N-differential graded algebras, and use these results to study N Lie algebroids.