Parafree Center-by-Metabelian Lie Algebras

Let L be a Lie algebra. Denote the second term of the derived series of L by L 00 . We define the parafree centre-by-metabelian Lie algebras. We prove that if L is a parafree centre-by-metabelian, then the center of L is L 00 . Moreover we show that the algebra L/L00 is parafree metabelian Lie algebra.

PDF

___

[1] Baumslag, G.: Groups with the Same Lower Central Sequence as a Relatively Free Group I. The Groups. Trans. Amer. Math. Soc., 129, 308-321 (1967).
[2] Baumslag, G.: Groups with the Same Lower Central Sequence as a Relatively Free Group. II Properties. Trans. Amer. Math. Soc. 142, 507-538 (1969).
[3] Baumslag, G.: Parafree Groups. Progress in Math. 248, 1-14 (2005).
[4] Baumslag, G., Cleary, S.: Parafree one-relator Groups. Journal of Group Theory. 9, 191-201 (2006).
[5] Baumslag, G., Cleary, S., Havas, G.: Experimenting with infinite group. Experimental Math. 13, 495-502 (2004).
[6] Baur, H.: Parafreie Lie Algebren und Homologie. Ph.D. thesis. Eidgenoessischen Technischen Hochschule Zuerich (1978).
[7] Baur, H.: A Note on Parafree Lie Algebras. Commun. in Algebra. 8(10), 953-960 (1980).
[8] Bokut, L.A., Kukin G. P.: Algorithmic and Combinatorial Algebra. Kluwer Academic Publishers. Dordrecht. The Netherlands (1994).
[9] Ekici, N., Velioğlu, Z.: Unions of Parafree Lie Algebras. Algebra. 2014, Article ID 385397, (2014).
[10] Ekici, N., Velioğlu, Z.: Direct Limit of Parafree Lie Algebras. Journal of Lie Theory. 25(2), 477-484 (2015).
[11] Velioğlu, Z.: Subalgebras and Quotient Algebras of Parafree Lie Algebras. IJPAM. 83, 507-517 (2013).
[12] Velioğlu, Z.: Parafree Metabelian Lie algebras which are Determined by Parafree Lie Algebras. Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat. 68(1), 883-888 (2019).

Mathematical Sciences and Applications E-Notes-Cover

ISSN: 2147-6268
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2013
Yayıncı: -

Arşiv