ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS

Year 2022, Volume: 5 Issue: 2, 61 - 67, 31.07.2022

Başak Erginkara , Şehmus Fındık

https://doi.org/10.33773/jum.1141787

https://izlik.org/JA37FC49DU

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

References

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