NECESSARY CONDITION FOR $IA$-AUTOMORPHISMS IN LEIBNIZ ALGEBRAS

Year 2024, Volume: 7 Issue: 2, 75 - 84, 31.07.2024

Zeynep Yaptı Özkurt

https://doi.org/10.33773/jum.1428190

Abstract

Let $F$ be the free Leibniz algebra generated by the set $%
X=\{x_{1},...,x_{n}\}$ over the field $K$ of characteristic $0$. consider $R$ as an
ideal of $F$. This study initially derives an explicit matrix representation for the $IA$-automorphisms of the Leibniz algebra $F/R^{\prime }$. Subsequently, we establish a necessary condition for an $IA$%
-endomorphism of $F/R^{\prime }$ to be an $IA$-automorphism. This method is explicitly based on Dieudonn\'{e} determinant.

Keywords

Leibniz algebra, Automorphisms, Dieudonné Determinant

Supporting Institution

Cukurova University BAP Coordination Council

Project Number

FBA-2020-13173

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