Seven-dimensional real and complex unsolvable Lie algebras (Q6587472)

The paper is devoted to a classification of \(7\)-dimensional unsolvable Lie algebras up to isomorphisms. The classification algorithm is based on the up-to conjugacy classification of the action of semisimple part on nilradical of dimension \(4\). In combination with some previous classifications [\textit{A. R. Parry}, A classification of real indecomposable solvable Lie algebras of small dimension with codimension one nil-radicals. Logan, UT: Utah State University (Master's thesis) (2007); \textit{F. Hindeleh} and \textit{G. Thompson}, Algebras Groups Geom. 25, No. 3, 243--265 (2008; Zbl 1210.17016); \textit{V. A. Le} et al., ``Classification of \(7\)-dimensional solvable Lie algebras having \(5\)-dimensional nil-radicals'', Preprint, \url{arXiv:2107.03990}], this provides a final classification of all \(7\)-dimensional unsolvable Lie algebras up-to isomorphisms.