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Metabelian Product of Parafree Lie Algebras, 2-Symmetric Words and Verbal Subalgebra Abstract

Year 2019, , 771 - 777, 31.08.2019
https://doi.org/10.18185/erzifbed.486996

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.

Paraserbest Lie Cebirlerinin Metabelyen Çarpımı, 2-Simetrik Kelimeler ve Verbal Altcebir

Year 2019, , 771 - 777, 31.08.2019
https://doi.org/10.18185/erzifbed.486996

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.
There are 7 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Makaleler
Authors

Zehra Velioğlu 0000-0001-7151-8534

Naime Ekici

Publication Date August 31, 2019
Published in Issue Year 2019

Cite

APA Velioğlu, Z., & Ekici, N. (2019). Paraserbest Lie Cebirlerinin Metabelyen Çarpımı, 2-Simetrik Kelimeler ve Verbal Altcebir. Erzincan University Journal of Science and Technology, 12(2), 771-777. https://doi.org/10.18185/erzifbed.486996

Cited By

Nilpotent Product of Parafree Lie Algebras and A Basis of This Product
Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Zehra VELİOGLU
https://doi.org/10.18185/erzifbed.633463