A remark on the linearization of nondegenerate Nambu structures of coorder 1

TL;DR

This paper demonstrates that Nambu structures of coorder 1 with a closed integrable form can always be linearized, including specific cases like unimodular Poisson structures with certain isotropy Lie algebras.

Contribution

It establishes a linearization result for Nambu structures of coorder 1 under the condition of admitting a closed integrable form, extending known linearization cases.

Findings

Nambu structures of coorder 1 can be linearized if they admit a closed integrable form.

Unimodular Poisson structures with isotropy Lie algebra rak{sl}(2,\u211d)} can be linearized.

The paper provides conditions under which linearization is always possible.

Abstract

In this note we show that Nambu structures of coorder 1 can always be linearized if they admit a closed integrable differential form. In particular, we show that a unimodular Poisson structure whose isotropy Lie algebra at a singular point is $\mathfrak{sl}(2,\mathbb{R})$, can always be linearized.