On vector-valued multisymplectic forms

TL;DR

This paper generalizes the local structure of vector-valued multisymplectic forms, shows they form a non-unital operad, and proves an entropy inequality for their partial compositions, advancing the mathematical understanding of multisymplectic geometry.

Contribution

It provides a standard local presentation for vector-valued multisymplectic forms and establishes their operadic structure, extending previous results for polysymplectic forms.

Findings

Vector-valued multisymplectic forms form a non-unital operad.

A standard local presentation for these forms is obtained.

An entropy inequality for partial compositions is proved.

Abstract

We obtain a standard local presentation for a vector-valued multisymplectic form on a smooth manifold, generalizing the known proof for polysymplectic forms. We show that vector-valued multisymplectic forms on a finite-dimensional real vector space form a non-unital operad. We prove an entropy inequality for partial compositions.