Nambu structures on four dimensional real Lie groups and related superintegrable systems

TL;DR

This paper classifies Nambu tensors on four-dimensional real Lie groups and constructs superintegrable systems using these structures as phase spaces with specific symmetry groups.

Contribution

It provides a complete classification of Nambu tensors of orders three and four on four-dimensional real Lie groups and demonstrates their application in building superintegrable systems.

Findings

All Nambu tensors of order three and four on four-dimensional real Lie groups are classified.

Superintegrable systems are constructed using Nambu structures on certain Lie groups.

The systems utilize symmetry groups A4;8 and A4;10 as phase space symmetries.

Abstract

We have determined all Nambu tensors (Nambu structures) of order four and three on four dimensional real Lie groups. Furthermore, we have obtained superintegrable systems by use of the Nambu structures of order four on some of these Lie groups as phase spaces with symmetry groups A4;8 and A4;10.