Existence and Uniqueness of Weak Homotopy Moment Maps

TL;DR

This paper extends classical symplectic geometry results on moment maps to the multisymplectic setting, demonstrating that their existence and uniqueness are governed by a Lie algebra cohomology complex.

Contribution

It generalizes the existence and uniqueness results of moment maps to weak homotopy moment maps in multisymplectic geometry, linking them to Lie algebra cohomology.

Findings

Existence and uniqueness of weak homotopy moment maps are governed by Lie algebra cohomology.

The cohomology complex reduces to the Chevalley-Eilenberg complex in symplectic geometry.

Classical results extend naturally to the multisymplectic context.

Abstract

In this paper we show that the classical results on the existence and uniqueness of moment maps in symplectic geometry generalize directly to weak homotopy moment maps in multisym- plectic geometry. In particular, we show that their existence and uniqueness is governed by a Lie algebra cohomology complex which reduces to the Chevalley-Eilenberg complex in the symplectic setup