Generalized Nambu system on S^3 and spinors

TL;DR

This paper explores the Nambu structure on the 3-sphere S^3, demonstrating its relation to SU(2) actions and spinors, and establishing a connection between Nambu systems and spinor representations.

Contribution

It introduces a natural Nambu structure on S^3 derived from a cross product and compares SU(2) actions on spinors with Nambu systems.

Findings

S^3 admits a natural Nambu structure from a cross product.

SU(2) acts as a Nambu action on S^3.

Comparison between SU(2) spinor actions and Nambu systems.

Abstract

It is shown that the manifold S^3 can be equipped with a natural Nambu structure arising out of a cross product on the tangent space. Further, the group action of SU(2) on S^3 is shown to be Nambu action. Moreover, we compare the action of SU(2) on spinors with that of a Nambu system.