Subregular subalgebras and invariant generalized complex structures on Lie groups

TL;DR

This paper introduces subregular subalgebras to classify Lie algebra subalgebras and constructs a non-regular invariant generalized complex structure on a Lie group, also classifying such structures for real forms of G2.

Contribution

It defines subregular subalgebras and applies this concept to construct and classify invariant generalized complex structures on Lie groups.

Findings

Constructed a non-regular invariant generalized complex structure.

Computed all invariant structures for real forms of G2.

Proposed subregular subalgebras as a classification tool.

Abstract

We introduce the notion of a subregular subalgebra, which we believe is useful for classification of subalgebras of Lie algebras. We use it to construct a non-regular invariant generalized complex structure on a Lie group. As an illustration of the study of invariant generalized complex structures, we compute them all for the real forms of G2.