Serbest Nilpotent Lie Cebirlerinin Otomorfizm Grupları Üzerine

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

Anahtar Kelimeler:

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

On The Automorphism Groups of Free Nilpotent Lie Algebras

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,

PDF

___

[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.