# Lie 2-algebra moment maps in multisymplectic geometry

## TL;DR

This paper introduces homotopy moment maps in multisymplectic geometry, extending the classical concept to Lie 2-algebras, with criteria for existence and cohomological construction methods.

## Contribution

It develops the theory of homotopy moment maps on Lie 2-algebras, generalizing classical moment maps in multisymplectic geometry and providing explicit existence criteria.

## Key findings

- Homotopy moment maps are characterized via cohomology.
- Existence criteria for homotopy moment maps are established.
- Construction methods for these maps are provided.

## Abstract

Consider a closed non-degenerate 3-form $\omega$ with an infinitesimal action of a Lie algebra $\mathfrak{g}$. Motivated by the fact that the observables associated to $\omega$ form a Lie 2-algebra, we introduce homotopy moment maps defined on a Lie 2-algebra rather than just on the Lie algebra $\mathfrak{g}$. We formulate existence criteria and provide a construction for such homotopy moment maps, by characterizing them in terms of cohomology.