ON THE GROUP OF POINTWISE INNER AUTOMORPHISMS

Authors : Ela Aydin

Pages : 221-226

Doi:10.33773/jum.1329709

View : 31 | Download : 26

Publication Date : 2023-07-31

Article Type : Research Article

Abstract :Let $L_{m,c}$ stand for the free metabelian nilpotent Lie algebra of class $c$ of rank $m$ over a field $K$ of characteristic zero. Automorphisms of the form $\\varphi(x_i)=e^{adu_i}(x_i)$ are called pointwise inner, where $e^{adu_i}$, is the inner automorphism induced by the element $u_i\\in L_{m,c}$ for each $i=1,\\ldots,m$. In the present study, we investigate the group structure of the group $\\text{\\rm PInn}(L_{m,c})$ of pointwise inner automorphisms of $L_{m,c}$ for low nilpotency classes.
Keywords : Lie algebras, metabelian, nilpotent, pointwise inner