POINTWISE INNER AUTOMORPHISMS OF RELATIVELY FREE LIE ALGEBRAS

Authors : Ela Aydin

Pages : 76-80

Doi:10.33773/jum.1140875

View : 26 | Download : 8

Publication Date : 2022-07-31

Article Type : Research

Abstract :Let $K$ be a field of characteristic zero, and $L_{m,c}$ be the free metabelian nilpotent Lie algebra of class $c$ of rank $m$ over $K$. We call an automorphism $\phi$ pointwise inner, if there exists an inner automorphism $\xi_i$ for each generator $x_i$, $i=1,\ldots,m$, such that $\phi(x_i)=\xi_i(x_i)$. In this study, we exemine the group $PI(L_{m,c})$ of pintwise inner automorphisms of the Lie algebra $L_{m,c}$, and we provide a set of generators for this group.
Keywords : Lie algebras, metabelian, nilpotent, piontwise inner