Normal automorphisms of free metabelian Leibniz algebras

Authors : Zeynep Yaptı Özkurt

Pages : 147-152

Doi:10.31801/cfsuasmas.1265768

View : 33 | Download : 86

Publication Date : 2024-03-16

Article Type : Research Paper

Abstract :Let $\\mathfrak{M}$ be a free metabelian Leibniz algebra generating set $X=\\{x_{1},...,x_{n}\\}$ over the field $\\mathfrak{K}$ of characteristic $0$. An automorphism $ \\phi $ of $\\mathfrak{M}$ is said to be normal automorphism if each ideal of $\\mathfrak{M}$ is invariant under $ \\phi $. In this work, it is proven that every normal automorphism of $\\mathfrak{M}$ is an IA-automorphism and the group of normal automorphisms coincides with the group of inner automorphisms.
Keywords : Leibniz algebra, normal automorphism, inner automorphism