Abstract
In this work, the metabelyen product of parafree Lie
algebras is defined and it is shown that this product is parafree. Let F be a
free Lie algebra of rank 2 and L be metabelian product of a finite number of
parafree abelyen Lie algebras. It is proved that the verbal subalgebra of L in
F equals F''. Moreover, by using this
result and Fox derivatives, all 2-symmetric words of L are determined.
References
- Baumslag, G. 1967. ‘’Groups with the same lower central sequence as a relatively free group I. The groups’’, Trans. Amer. Math. Soc., 129, 308-321.
- Baumslag, G. 1969. ‘’Groups with the same lower central sequence as a relatively free group. II Properties’’, Trans. Amer. Math. Soc., 142, 507-538.
- Baur, H. (1978). ‘’Parafreie Liealgebren und homologie’’, Diss. Eth Nr., Zurich, 6126, 60p.
- Bryant, R.M. and Roman’kov, V.A. 1999. ‘’Automorphism groups of relatively free groups’’, Math. Proc. Camb. Phil. soc., 127(3), 411-424.
- Fox, R.H. 1953. ‘’Free differential calculus. I. Derivations in the free group ring’’, Ann. Math. 57(3), 547-560.
- Pan, J. 2006. ‘’On 2-Symmetric words and verbal subgroup of metabelian product of abelian groups’’, Alg. Colloquium, 13(3), 535-540.
- Shmel’kin, A.L. and Syrtsov, A.V. 2005. ‘’On embeddings of some factor algebras of free sums of Lie algebras’’, J. Math. Sci. 13( 6), 6148-6152.
Abstract
Bu çalışmada paraserbest Lie cebirlerinin metabelyen
çarpımı tanımlanmış ve bu çarpımın paraserbest olduğu gösterilmiştir. F rankı 2
olan bir serbest Lie cebiri ve L sonlu sayıda paraserbest abelyen Lie
cebirlerinin metabelyen çarpımı olmak üzere F de L tarafından tanımlanan verbal
alt cebirin F'' olduğu ispatlanmıştır. Ayrıca bu sonuç ve Fox türevleri
kullanılarak L nin bütün 2-simetrik kelimelerinin belirlenebileceği
gösterilmiştir.
References
- Baumslag, G. 1967. ‘’Groups with the same lower central sequence as a relatively free group I. The groups’’, Trans. Amer. Math. Soc., 129, 308-321.
- Baumslag, G. 1969. ‘’Groups with the same lower central sequence as a relatively free group. II Properties’’, Trans. Amer. Math. Soc., 142, 507-538.
- Baur, H. (1978). ‘’Parafreie Liealgebren und homologie’’, Diss. Eth Nr., Zurich, 6126, 60p.
- Bryant, R.M. and Roman’kov, V.A. 1999. ‘’Automorphism groups of relatively free groups’’, Math. Proc. Camb. Phil. soc., 127(3), 411-424.
- Fox, R.H. 1953. ‘’Free differential calculus. I. Derivations in the free group ring’’, Ann. Math. 57(3), 547-560.
- Pan, J. 2006. ‘’On 2-Symmetric words and verbal subgroup of metabelian product of abelian groups’’, Alg. Colloquium, 13(3), 535-540.
- Shmel’kin, A.L. and Syrtsov, A.V. 2005. ‘’On embeddings of some factor algebras of free sums of Lie algebras’’, J. Math. Sci. 13( 6), 6148-6152.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | August 31, 2019 |
| Published in Issue | Year 2019 |