Capability of Nilpotent Lie algebras with small derived Subalgebra
Peyman Niroomand, Mohsen Parvizi
TL;DR
This paper classifies all capable nilpotent Lie algebras with a derived subalgebra of dimension at most one, providing a complete understanding of their structure in this specific case.
Contribution
It offers a complete classification of capable nilpotent Lie algebras with small derived subalgebras, a previously unresolved problem.
Findings
All capable nilpotent Lie algebras with derived subalgebra of dimension ≤1 are classified.
The structure of these Lie algebras is fully characterized.
The classification aids in understanding the capability property in nilpotent Lie algebras.
Abstract
In this paper, we classify all capable nilpotent Lie algebras with derived subalgebra of dimension at most 1.
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