Capable Lie algebras with the derived subalgebra of dimension two over an arbitrary field

TL;DR

This paper classifies capable nilpotent Lie algebras with a two-dimensional derived subalgebra over any field, providing explicit structures especially for class 3 algebras.

Contribution

It offers a complete classification of capable nilpotent Lie algebras with derived subalgebra of dimension two, including explicit structures for class 3 cases.

Findings

Classification of capable nilpotent Lie algebras with derived subalgebra of dimension two

Explicit structures for class 3 capable Lie algebras

Applicable over arbitrary fields

Abstract

In this paper, we classify all capable nilpotent Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field. Moreover, the explicit structure of such Lie algebras of class 3 is given.