The Polynilpotent Multiplier of Lie Algebras

Abstract

Let [Formula: see text] be the variety of polynilpotent Lie algebras of class row (c1, …, cn). The paper is devoted to present the concepts of polynilpotent multiplier [Formula: see text] and cover of a Lie algebra L with respect to the variety [Formula: see text], and compute [Formula: see text] for some known Lie algebras. Also, we determine the structure of all covers of Lie algebras whose polynilpotent multipliers are finite-dimensional, and investigate some common properties between covers.