ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS

Authors : Başak Erginkara, Şehmus Findik

Pages : 61-67

Doi:10.33773/jum.1141787

View : 25 | Download : 7

Publication Date : 2022-07-31

Article Type : Research

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 $\text{\rm C}(\text{\rm Inn}(F_m))$ of inner automorphism group $\text{\rm Inn}(F_m)$ of $F_m$ in $\text{\rm Aut}(F_m)$. We provide an elementary proof to show that $\text{\rm C}(\text{\rm Inn}(F_m))=\text{\rm Inn}(F_m)$.
Keywords : Automorphism, inner, Lie algebras