Seven-dimensional real and complex unsolvable Lie algebras

This paper is devoted to the classification up to isomorphism of abstract unsolvable Lie algebras of dimension $7$. With the help of Maltsev splitting, the problem of describing Lie algebras over a field of characteristic zero is reduced to describing almost algebraic Lie algebras, which, in turn, require knowledge of semisimple and nilpotent algebras. Based on the classifications of semisimple and nilpotent Lie algebras, the paper presents an algorithm for describing abstract Lie algebras and conducts the classification of seven-dimensional unsolvable Lie algebras over fields ${\mathbb R}$ and ${\mathbb C}$.