Classification of linearly compact simple Nambu-Poisson algebras

TL;DR

This paper introduces a universal superalgebra concept and uses it to classify simple linearly compact n-Nambu-Poisson algebras over algebraically closed fields of characteristic zero.

Contribution

It generalizes previous constructions to define a universal odd generalized Poisson superalgebra and provides a complete classification of simple linearly compact n-Nambu-Poisson algebras.

Findings

Complete classification of simple linearly compact n-Nambu-Poisson algebras

Introduction of universal odd generalized Poisson superalgebra

Generalization of previous algebraic constructions

Abstract

We introduce the notion of universal odd generalized Poisson superalgebra associated to an associative algebra A, by generalizing a construction made in [5]. By making use of this notion we give a complete classification of simple linearly compact (generalized) n-Nambu-Poisson algebras over an algebraically closed field of characteristic zero.