Graded contractions of g2

TL;DR

This paper classifies graded contractions of the fine ^3-grading on the complex Lie algebra g2, revealing a large family of solvable 14-dimensional Lie algebras through a detailed classification.

Contribution

It provides a comprehensive classification of graded contractions of g2's fine ^3-grading, including equivalence and strong equivalence, and introduces new solvable Lie algebras.

Findings

Classified graded contractions of g2^3-grading

Identified a large family of 14-dimensional solvable Lie algebras

Established equivalence and strong equivalence relations

Abstract

Graded contractions of the fine $\mathbb{Z}_2^3$-grading on the complex exceptional Lie algebra $\mathfrak{g}_2$ are classified up to equivalence and up to strongly equivalence. In particular, a large family of 14-dimensional Lie algebras arise, most of them solvable.