Serbest Nilpotent Lie Cebirlerinin Otomorfizm Grupları Üzerine

??,? karakteristiği sıfır olan bir cisim üzerinde sonlu ?, ? ≥ 2 rankına sahip, ? −yıncı sınıftan serbest nilpotent Lie cebiri olsun. ??,? nın merkezi otomorfizmler grubunun bu cebirin ?? −otomorfizmler grubu ile iç otomorfizmler grubuna eşit olması için gerek ve yeter koşulları belirledik.

On The Automorphism Groups of Free Nilpotent Lie Algebras

Let ??,? be the free nilpotent Lie algebra of class ? that of finite rank ?, ? ≥ 2 over a field of characteristic zero. In this study, we give necessary and sufficient conditions on the equalities of the central automorphisms group of ??,? to the IAautomorphisms group and inner automorphisms group of ??,?.

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[1] J. E. Adney, T. Yen, “Automorphisms of p-groups”, Illinois J. Math. 9, pp. 137-143, 1965.
[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 centerby-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.