Nilpotent Product of Parafree Lie Algebras and A Basis of This Product

Öz

In this work, n-th nilpotent and minimal nilpotent products of parafree Lie algebras are examined and it is shown that these products are parafree. Also, a base set is obtained for the n-th nilpotent products of  two abelian Lie algebras that are nilpotent of class n.In this work, n-th nilpotent and minimal nilpotent products of parafree Lie algebras are examined and it is shown that these products are parafree. Also, a base set is obtained for the n-th nilpotent products of two abelian Lie algebras that are nilpotent of class n. In this work, n-th nilpotent and minimal nilpotent products of parafree Lie algebras are examined and it is shown that these products are parafree. Also, a base set is obtained for the n-th nilpotent products of two abelian Lie algebras that are nilpotent of class n.

Anahtar Kelimeler

• Parafree Lie algebras
• Free Lie Algebras
• Nlpotent Product

Nilpotent Product of Parafree Lie Algebras and A Basis of This Product

Öz

In this work, n-th nilpotent and minimal nilpotent products of parafree Lie algebras are examined and it is shown that these products are parafree. Also, a base set is obtained for the n-th nilpotent products of two abelian Lie algebras that are nilpotent of class n. In this work, n-th nilpotent and minimal nilpotent products of parafree Lie algebras are examined and it is shown that these products are parafree. Also, a base set is obtained for the n-th nilpotent products of two abelian Lie algebras that are nilpotent of class n.In this work, n-th nilpotent and minimal nilpotent products of parafree Lie algebras are examined and it is shown that these products are parafree. Also, a base set is obtained for the n-th nilpotent products of two abelian Lie algebras that are nilpotent of class n.

Anahtar Kelimeler

• Parafree Lie algebras,
• Free Lie Algebras
• Nilpotent product

Kaynakça

1. Akdoğan, N., 2014. Serbest Lie Cebirlerinin Çarpımları ve Rezidülü-P Cebirleri, Master Thesis, Çukurova Uni., Adana.
2. 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.
3. Baumslag, G., Groups with the same lower central sequence as a relatively free group. II Properties, Trans. Amer. Math. Soc., 142, 507-538, 1969.
4. Baur, H., Parafreie Lie algebren und homologie, Diss. Eth Nr., 6126, 1978.
5. Golovin, O.N. 1950, Nilpotent Product of Groups. Mat. Sb. (N.S.), 27(69):3, 427-454.
6. Velioğlu, Z., 2013. Paraserbest Lie Cebirleri, Ph.D Thesis, Çukurova Uni., Adana.
7. Velioğlu, Z., and Ekici, N., 2019, Paraserbest Lie Cebirlerinin Metabelyen Çarpımı, 2-Simetrik Kelimeler ve Verbal Altcebir, Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 12(2), 771-777.
8. Velioğlu, Z., 2019, Soluble Product of Parafree Lie algebras and Its Residual Properties, Applied Mathematics and Nonlinear Sciences, 4(1) , 1–5.