Necessary Condition for $IA$-Automorphisms in Leibniz Algebras

Let F be the free Leibniz algebra generated by the set % X=₁,...,xₙ\ 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. Subsequently, we establish a necessary condition for an $IA$% -endomorphism of F/R to be an $IA$-automorphism. This method is explicitly based on Dieudonn\'{e} determinant.