ON THE GROUP OF POINTWISE INNER AUTOMORPHISMS

Year 2023, Volume: 6 Issue: 2, 221 - 226, 31.07.2023

Ela Aydın

https://doi.org/10.33773/jum.1329709

Cited By: 1

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

References

• Y. A. Bahturin, Identical Relations in Lie Algebras (Russian), ”Nauka”, Moscow, 1985. Translation: VNU Science Press, Utrecht, (1987).
• V. Drensky, Free Algebras and PI-Algebras, Springer, Singapore, (1999).
• E. Aydın, Pointwise inner automoprphisms of relatively free Lie algebras, Journal of Universal Mathematics, Vol.5, No.2, pp.76-80 (2022).