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

TitleOn some relationships between the factors of the canonical central series of Leibniz algebras
Publication TypeJournal Article
Year of Publication2016
AuthorsKurdachenko, LA, Otal, J, Pypka, AA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2016.03.014
Issue3
SectionMathematics
Pagination14-18
Date Published3/2016
LanguageUkrainian
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.
KeywordsLeibniz 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