On some relationships between the factors of the canonical central series of Leibniz algebras

1Kurdachenko, LA, 1Otal, J, 1Pypka, AA
1Oles Honchar Dnipropetrovsk National University
Dopov. Nac. akad. nauk Ukr. 2016, 3:14-18
https://doi.org/10.15407/dopovidi2016.03.014
Section: Mathematics
Language: Ukrainian
Abstract: 
We have proved that the finiteness of the codimension of some member $\zeta_{k}(L)$ of the upper central series of the Leibniz algebra $L$ yields the finiteness of the dimension of $\gamma_{k+1}(L)$ and give the bounds of this finiteness.
Keywords: Leibniz algebra, Lie algebra, lower central series, upper central series
References: 
  1. Loday J. L. Enseign. Math., 1993, 39: 269–293.
  2. Albeverio S. A., Ayupov Sh. A., Omirov B. A. Commun. Algebra, 2005, 33: 159–172. https://doi.org/10.1081/AGB-200040932
  3. Barnes D. Commun. Algebra, 2011, 39: 2463–2472. https://doi.org/10.1080/00927872.2010.489529
  4. Barnes D. Bull. Australian Math. Soc, 2012, 86: 184–185. https://doi.org/10.1017/S0004972711002954
  5. Barnes D. Commun. Algebra, 2012, 40: 1388–1389. https://doi.org/10.1080/00927872.2010.551532
  6. Barnes D. Commun. Algebra, 2013, 41: 4046–4065. https://doi.org/10.1080/00927872.2012.700978
  7. Patsourakos A. Commun. Algebra, 2007, 35: 3828–3834. https://doi.org/10.1080/00927870701509099
  8. Ray C. B., Combs A., Gin N., Hedges A., Hird J. T., Zack L. Commun. algebra, 2014, 42: 2404–2410. https://doi.org/10.1080/00927872.2012.717655
  9. Stewart I. N. Proc. London Math. Soc., 1974, 28: 129–140. https://doi.org/10.1112/plms/s3-28.1.129
  10. Baer R. Math. Ann., 1952, 124: 161–177. https://doi.org/10.1007/BF01343558
  11. Vaughan-Lee M. R. J. London Math. Soc., 1972, 5: 673–680. https://doi.org/10.1112/jlms/s2-5.4.673
  12. Neumann B. H. Proc. London Math. Soc., 1951, 1: 178–187. https://doi.org/10.1112/plms/s3-1.1.178