On The Automorphism Groups of Free Nilpotent Lie Algebras

Year 2019, Volume: 7 Issue: 3, 403 - 405, 28.09.2019

Özge Öztekin , Cennet Eskal

https://doi.org/10.21541/apjes.552208

Abstract

Let L_(m,k) be the free nilpotent of class k Lie algebra of finite rank m, m≥2 over a field of characteristic zero. In this study, we give necessary and sufficient conditions on  the equalities of the central automorhisms group of L_(m,k) to the IA-automorphisms group and inner automorphisms group of L_(m,k)

Keywords

Free Lie algebra , , IA-automorphisms group , inner automorphisms group , central automorphisms group

Serbest Nilpotent Lie Cebirlerinin Otomorfizm Grupları Üzerine

Abstract

L_m,k karakteristiği sıfır olan bir cisim üzerinde
sonlu m,m>2 rankına sahip, k- yıncı sınıftan
serbest nilpotent Lie cebiri
olsun.L_m,k nın IA- otomorfizm
grubu ile iç otomorfizm grubunun merkezi otomorfizm grubuna eşit olması için gerek
ve yeter koşulları belirledik.

Keywords

Serbest Lie cebir , IA-otomorfizm grubu , iç otomorfizm grubu , merkezi otomorfizm grubu

References

• [1] J. E. AdneyT.Yen, Automorphisms of p-groups, Illinois J. Math. 9(1965), 137-143.
• [2] M. S. Attar, “On central automorphisms that fix the centre elementwise”, Arch. Math., vol. 89, pp. 296-297, 2007.
• [3] M. J. Curran, “Finite groups with central automorphism group of minimal order”, Math. Proc. R. Ir. Acad., vol. 104, no. A2, pp. 223-229, 2004.
• [4] M. J. Curran, D. J. McCaughnan, “Central automorphisms that are almost inner”, Communications in Algebra, vol. 29, no. 5, pp. 2081-2087, 2001.
• [5] M. Drensky, “Automorphisms of free nilpotent Lie algebras Can. J. Math., vol. 13, no. 2, pp. 259-279, 1990.
• [6] Z. Esmerligil, “On central automorphisms of free center-by-metabelian Lie algebras”, IARJSET, vol. 3, no. 7, 2016.
• [7] Ş. Fındık, “Normal and normally outer automorphisms of free metabelian nilpotent Lie algebras”, Serdica Math. J, 36, pp. 170-210, 2010.
• [8] G. Mashevitzky, B. Plotkin, E. Plotkin, “Automorphisms of the category of free Lie algebras”, Journal of Algebra, vol. 283, no. 2, pp. 490-512, 2004.
• [9] Ö. Öztekin, N. Ekici, “Central automorphisms of free nilpotent Lie algebras”, Journal of Algebra and its Applications, Doi. 1750205., 2016.
• [10] V. Romankov, “On the automorphism group of a free metabelian Lie algebra”, International Journal of Algebra and Computation, vol. 18, no. 1, pp. 1–18, 2008.