Normal automorphisms of free metabelian Leibniz algebras

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

References

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