Classification of Lie algebras with naturally graded quasi-filiform nilradicals

The whole class of complex Lie algebras gg having a naturally graded nilradical with characteristic sequence c(g)=(dimg−2,1,1)c(g)=(dimg−2,1,1) is classified. It is shown that up to one exception, such Lie algebras are solvable.

► The derivations of nilpotent algebras of nilindex (n−2,1,1)(n−2,1,1) are determined.
► The extensions of these nilpotent algebras by the derivations are fully classified.
► The solvability properties and Levi subalgebras of the extensions are analyzed.