On the Schur Lie-multiplier and Lie-covers of Leibniz n-algebras

Document Type

Article

Publication Date

1-1-2023

Publication Title

Communications in Algebra

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 (Formula presented.) -multiplier and (Formula presented.) -covers on Leibniz n-algebras. We provide a characterization of (Formula presented.) -perfect Leibniz n-algebras by means of universal (Formula presented.) -central extensions. It is also provided some inequalities on the dimension of the Schur (Formula presented.) -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 (Formula presented.) -commutator of a Leibniz n-algebra with finite dimensional (Formula presented.) -central factor, and also for the dimension of the Schur (Formula presented.) -multiplier of a finite dimensional Leibniz n-algebra.

Department

Mathematics

Volume Number

51

Issue Number

2

First Page

729

Last Page

741

DOI

10.1080/00927872.2022.2113400

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