On Parafree Leibniz Algebras

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Celal Bayar Üniversitesi Fen Bilimleri Dergisi
Volume:18 Issue:3
On Parafree Leibniz Algebras

On Parafree Leibniz Algebras

Authors : Nil MANSUROĞLU

Pages : 275-278

Doi:10.18466/cbayarfbe.1072438

View : 21 | Download : 12

Publication Date : 2022-09-29

Article Type : Research Paper

Abstract :The parafree Leibniz algebras are a special class of Leibniz algebras which have many properties with a free Leibniz algebra. In this note, we introduce the structure of parafree Leibniz algebras. We survey the important results in parafree Leibniz algebras which are analogs of corresponding results in parafree Lie algebras. We first investigate some properties of subalgebras and quotient algebras of parafree Leibniz algebras. Then, we describe the direct sum of parafree Leibniz algebras. We show that the direct sum of two parafree Leibniz algebras is a Leibniz algebra. Furthermore, we prove that the direct sum of two parafree Leibniz algebras is again parafree.
Keywords : Parafree Leibniz algebra, subalgebras, quotient algebras, direct sum

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