A different perspective on H-like Lie algebras

TL;DR

This paper offers a new linear algebraic framework for understanding H-like Lie algebras, introduces novel construction methods, and classifies those with rank-two associated maps, advancing the structural theory of these algebras.

Contribution

It characterizes H-like Lie algebras via subspaces of cones over conjugacy classes, providing new construction techniques and a classification for certain rank conditions.

Findings

Characterization of H-like Lie algebras through linear algebraic subspaces

Development of new construction methods including tensor products and central sums

Classification of H-like Lie algebras with rank-two $J_Z$-maps

Abstract

We characterize H-like Lie algebras in terms of subspaces of cones over conjugacy classes in $\mathfrak{so}(\mathbb{R}^q)$, translating the classification problem for H-like Lie algebras to an equivalent problem in linear algebra. We study properties of H-like Lie algebras, present new methods for constructing them, including tensor products and central sums, and classify H-like Lie algebras whose associated $J_Z$-maps have rank two for all nonzero $Z$.