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

Authors

  • L. A. Kurdachenko Oles Honchar Dnipropetrovs’k National University
  • J. Otal Oles Honchar Dnipropetrovs’k National University
  • A. A. Pypka Oles Honchar Dnipropetrovs’k National University

DOI:

https://doi.org/10.15407/dopovidi2016.03.014

Keywords:

Leibniz algebra, Lie algebra, lower central series, upper central series

Abstract

We have proved that the finiteness of the codimension of some member ζk(L) of the upper central series of the Leibniz algebra L yields the finiteness of the dimension of γk+1(L) and give the bounds of this finiteness

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References

Loday J. L. Enseign. Math., 1993, 39: 269–293.

Albeverio S. A., Ayupov Sh. A., Omirov B. A. Commun. Algebra, 2005, 33: 159–172. https://doi.org/10.1081/AGB-200040932

Barnes D. Commun. Algebra, 2011, 39: 2463–2472. https://doi.org/10.1080/00927872.2010.489529

Barnes D. Bull. Australian Math. Soc, 2012, 86: 184–185. https://doi.org/10.1017/S0004972711002954

Barnes D. Commun. Algebra, 2012, 40: 1388–1389. https://doi.org/10.1080/00927872.2010.551532

Barnes D. Commun. Algebra, 2013, 41: 4046–4065. https://doi.org/10.1080/00927872.2012.700978

Patsourakos A. Commun. Algebra, 2007, 35: 3828–3834. https://doi.org/10.1080/00927870701509099

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

Stewart I. N. Proc. London Math. Soc., 1974, 28: 129–140. https://doi.org/10.1112/plms/s3-28.1.129

Baer R. Math. Ann., 1952, 124: 161–177. https://doi.org/10.1007/BF01343558

Vaughan-Lee M. R. J. London Math. Soc., 1972, 5: 673–680. https://doi.org/10.1112/jlms/s2-5.4.673

Neumann B. H. Proc. London Math. Soc., 1951, 1: 178–187. https://doi.org/10.1112/plms/s3-1.1.178

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Published

10.10.2024

How to Cite

Kurdachenko, L. A., Otal, J., & Pypka, A. A. (2024). On some relationships between the factors of the canonical central series of Leibniz algebras . Reports of the National Academy of Sciences of Ukraine, (3), 14–18. https://doi.org/10.15407/dopovidi2016.03.014

Issue

No. 3 (2016): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

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