Polynilpotent capability of a pair of Lie algebras

Abstract

The notion of capability for pairs of groups was defined by Ellis in 1996. Also, the concept of capability of Lie algebras was introduced by some authors, and is analogous to the group case. In this paper, we generalize the concept of capability of a Lie algebra $L$ to the polynilpotent capability of a pair $(N,L)$ of Lie algebras and introduce a criterion for polynilpotent capability of $(N,L)$.