ON THE GROUP OF POINTWISE INNER AUTOMORPHISMS

Authors : Ela AYDIN

Pages : 221-226

Doi:10.33773/jum.1329709

View : 31 | Download : 27

Publication Date : 2023-07-31

Article Type : Research Paper

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 $\\varphiinsert ignore into journalissuearticles values(x_i);=e^{adu_i}insert ignore into journalissuearticles values(x_i);$ 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 $\\text{\\rm PInn}insert ignore into journalissuearticles values(L_{m,c});$ of pointwise inner automorphisms of $L_{m,c}$ for low nilpotency classes.
Keywords : Lie algebras, metabelian, nilpotent, pointwise inner