Local automorphisms on finite-dimensional Lie and Leibniz algebras (1803.03142v2)

Abstract: We prove that a linear mapping on the algebra (\mathfrak{sl}_n) of all trace zero complex matrices is a local automorphism if and only if it is an automorphism or an anti-automorphism. We also show that a linear mapping on a simple Leibniz algebra of the form (\mathfrak{sl}_n\dot +\mathcal{I}) is a local automorphism if and only if it is an automorphism. We give examples of finite-dimensional nilpotent Lie algebras (\mathcal{L}) with (\dim \mathcal{L} \geq 3) which admit local automorphisms which are not automorphisms.