ABOUT GROUP OF POINTWISE INNER AUTOMORPHISMS FOR NILPOTENCY CLASS FOUR

Yıl 2023, , 58 - 61, 15.10.2023

Ela Aydın

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

Öz

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.

Anahtar Kelimeler

Lie algebras, metabelian, nilpotent, pointwise inner.

Kaynakça

• Yu.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).
• V. Drensky, S_. F_nd_k, Inner and outer automorphisms of free metabelian nilpotent Lie algebras. Communications in Algebra, Vol.40, No.12, pp.4389-4403 (2012).
• E. Aydin, Pointwise inner automoprphisms of relatively free Lie algebras, Journal of Universal Mathematics, Vol.5, No.2, pp.76-80 (2022).
• E. Aydin, On the Group of Pointwise Inner Automoprphisms, Journal of Universal Mathematics, Vol.6, No.2, pp.221-226 (2023).
• Ş Findik, Normal and normally outer automorphisms of free metabelian nilpotent Lie algebras, Serdica Mathematical Journal, Vol.35, No.2, pp.171-210 (2010).