ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS

Authors : Başak ERGİNKARA, Şehmus FINDIK

Pages : 61-67

Doi:10.33773/jum.1141787

View : 23 | Download : 10

Publication Date : 2022-07-31

Article Type : Research Paper

Abstract :Let $F_m$ be the free metabelian Lie algebra of rank $m$ over a field $K$ of characteristic 0. An automorphism $\varphi$ of $F_m$ is called central if $\varphi$ commutes with every inner automorphism of $F_m$. Such automorphisms form the centralizer $\text{\rm C}insert ignore into journalissuearticles values(\text{\rm Inn}insert ignore into journalissuearticles values(F_m););$ of inner automorphism group $\text{\rm Inn}insert ignore into journalissuearticles values(F_m);$ of $F_m$ in $\text{\rm Aut}insert ignore into journalissuearticles values(F_m);$. We provide an elementary proof to show that $\text{\rm C}insert ignore into journalissuearticles values(\text{\rm Inn}insert ignore into journalissuearticles values(F_m););=\text{\rm Inn}insert ignore into journalissuearticles values(F_m);$.
Keywords : Automorphism, inner, Lie algebras