Başak ERGİNKARA, Şehmus FINDIK

ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS

ISSN: 2618-5660
Başlangıç: 2018
Yayıncı: Gökhan ÇUVALCIOĞLU

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,

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