Abstract
In this article, we study the notion of central extensions of Leibniz n-algebras relative to n-Lie algebras to study properties of Schur -multiplier and -covers on Leibniz n-algebras. We provide a characterization of -perfect Leibniz n-algebras by means of universal -central extensions. It is also provided some inequalities on the dimension of the Schur -multiplier of Leibniz n-algebras. Analogue to Wiegold and Green results on groups or Moneyhun results on Lie algebras, we provide upper bounds for the dimension of the -commutator of a Leibniz n-algebra with finite dimensional -central factor, and also for the dimension of the Schur -multiplier of a finite dimensional Leibniz n-algebra.
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