On Parafree Leibniz Algebras

Year 2022, Volume: 18 Issue: 3, 275 - 278, 29.09.2022

Nil Mansuroğlu

https://doi.org/10.18466/cbayarfbe.1072438

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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