ABOUT GROUP OF POINTWISE INNER AUTOMORPHISMS FOR NILPOTENCY CLASS FOUR

Year 2023, , 58 - 61, 15.10.2023

Ela Aydın

https://doi.org/10.33773/jum.1372208

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 $\text{\rm PInn}(L_{m,4})$ of pointwise inner automorphisms of $L_{m,4}$ for nilpotency class four.

Keywords

Lie algebras, metabelian, nilpotent, pointwise inner.

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