Abstract
Given a non-negative integer [Formula: see text], we study two different notions of the [Formula: see text]-capability of Lie algebras via the non-abelian [Formula: see text]-exterior product of Lie algebras. The first is related to the [Formula: see text]-crossed modules and inner [Formula: see text]-derivations, and the second is the Lie algebra version of the [Formula: see text]-capability of groups proposed by Ellis in 1995.
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