Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals

TL;DR

This paper classifies 7-dimensional solvable Lie algebras with 5-dimensional nilradicals, combining previous results to provide a comprehensive taxonomy of such algebras over real and complex fields.

Contribution

It offers a complete classification of 7-dimensional indecomposable solvable Lie algebras with 5-dimensional nilradicals, integrating multiple prior studies.

Findings

Complete classification of 7D solvable Lie algebras with 5D nilradicals.

Unified framework combining previous classifications.

Extension of classifications to both real and complex cases.

Abstract

This paper presents a classification of 7-dimensional real and complex indecomposable solvable Lie algebras having some 5-dimensional nilradicals. Afterwards, we combine our results with those of Rubin and Winternitz (1993), Ndogmo and Winternitz (1994), Snobl and Winternitz (2005, 2009), Snobl and Kar\'asek (2010) to obtain a complete classification of 7-dimensional real and complex indecomposable solvable Lie algebras with 5-dimensional nilradicals. In association with Gong (1998), Parry (2007), Hindeleh and Thompson (2008), we achieve a classification of 7-dimensional real and complex indecomposable solvable Lie algebras.