Polynilpotent capability of Lie algebras

Abstract

Abstract Let be the variety of polynilpotent Lie algebras of class row . In this article, we generalize the Ganea map and the notion of capability with respect to the variety , and study their connections with the polynilpotent multipliers of Lie algebras. Furthermore, We determine the polynilpotent multipliers of some known Lie algebras and give the structure of all -capable nilpotent Lie algebras with derived subalgebra of dimension at most 1.