POINTWISE INNER AUTOMORPHISMS OF RELATIVELY FREE LIE ALGEBRAS

Year 2022, Volume: 5 Issue: 2, 76 - 80, 31.07.2022

Ela Aydın

https://doi.org/10.33773/jum.1140875

Cited By: 2

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

References

• G. Endimioni, Inner automorphisms of free nilpotent groups, The Quarterly Journal of Mathematics, 53 (4), pp. 397-402 (2002). Ş. Fındık, Normal and Normally outher automorphisms of free metabelian nilpotent Lie algebra, Serdica Math J., 36, pp. 171-210 (2010).
• F.K. Grossman, On the residual Finiteness of certain mapping class groups, J. Londan Mathematical Soc., 9, pp. 160-164 (1974). A. Lubotzky, Normal Automorphisms of free groups, J. Algebra, 63, pp. 494-498 (1980). A. Temizyürek, E. Aydın, Serbest Metabelyen Lie Cebirlerinin noktasal iç otomorfizmleri, Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, pp. 127-134 (2004).