A Nearly Quaternionic Structure on SU(3)

TL;DR

The paper demonstrates that the compact Lie group SU(3) admits a special quaternionic-like structure characterized by a differential ideal generated by three specific 2-forms, achieved through a reduction to an SO(3) subgroup.

Contribution

It introduces a nearly quaternionic structure on SU(3) with a differential ideal, expanding understanding of geometric structures on Lie groups.

Findings

SU(3) admits an Sp(2)Sp(1)-structure

The structure is characterized by three 2-forms spanning a differential ideal

Reduction to an SO(3) subgroup is key to the construction

Abstract

It is shown that the compact Lie group SU(3) admits an Sp(2)Sp(1)-structure whose distinguished 2-forms $\omega_1,\omega_2,\omega_3$ span a differential ideal. This is achieved by first reducing the structure further to a subgroup isomorphic to SO(3).