NECESSARY CONDITION FOR $IA$-AUTOMORPHISMS IN LEIBNIZ ALGEBRAS

Authors : Zeynep Yaptı Özkurt

Pages : 75-84

Doi:10.33773/jum.1428190

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Publication Date : 2024-07-31

Article Type : Research Paper

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