A remark on calibrations and Lie groups

TL;DR

This paper explores the geometric structure of simple Lie groups by identifying special subspaces related to principal three-dimensional subgroups and investigates their calibration properties with respect to invariant forms.

Contribution

It introduces a novel approach using principal three-dimensional subgroups to analyze calibration properties of subspaces within Lie algebras.

Findings

Identified special subspaces of Lie algebras associated with principal three-dimensional subgroups.

Determined conditions under which these subspaces are calibrated by invariant forms.

Provided insights into the geometric and algebraic structure of simple Lie groups.

Abstract

We use the notion of the principal three-dimensional subgroup of a simple Lie group to identify certain special subspaces of the Lie algebra and address the question of whether these are calibrated for invariant forms on the group.