Lie algebras obtained as extensions by derivations of the nilpotent algebra \({\mathcal L}_{5, 3}\) (Q2875952)

Let \({\mathcal L}_{5,3}\) be the nilpotent Lie algebra over \({\mathbb R}\) defined by a basis \(X_0,X_1,X_2,X_3,X_4\) satisfying the commutation relations \([X_0,X_1]=X_2\), \([X_0,X_2]=X_3\), \([X_1,X_2]=X_4\). This Lie algebra can be singled out in various ways, for instance it is the only quasi-filiform Lie algebra that admits an associative bilinear non-degenerate form. The main result of the paper under review is a classification of all real non-split Lie algebras whose nilradical is isomorphic to \({\mathcal L}_{5,3}\). Generalized Casimir invariants of these Lie algebras are studied as well.NEWLINENEWLINEFor the entire collection see [Zbl 1287.00022].