A survey on partial Nambu-Poisson structures in the convenient setting

TL;DR

This survey explores partial Nambu-Poisson structures in infinite-dimensional convenient spaces, discussing their properties, generalizations, and limits, providing a comprehensive overview of this mathematical framework.

Contribution

It offers a comprehensive overview of partial Nambu-Poisson structures in infinite dimensions, including their properties, generalizations, and limit constructions.

Findings

Characterization of the associated characteristic distribution

Analysis of projective and direct limits of these structures

Connections to partial Poisson and Nambu-Poisson structures

Abstract

This paper is a survey (may be incomplete) on partial Nambu-Poisson structures in infinite dimension, mainly in the convenient setting. These ones can be seen as a generalization of both partial Poisson and Nambu-Poisson structures. We also study the properties of the associated characteristic distribution. Finally, we are interested in the projective and direct limits of such structures.