On some reciprocal relations between the factors of the upper and lower central series in Lie algebras

TitleOn some reciprocal relations between the factors of the upper and lower central series in Lie algebras
Publication TypeJournal Article
Year of Publication2015
AuthorsKurdachenko, LA, Pypka, AA, Subbotin, IYa.
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2015.05.021
Issue5
SectionMathematics
Pagination21-25
Date Published5/2015
LanguageUkrainian
Abstract

A generalization of the group-theoretic Baer's theorem regarding relations between the factors of the upper and lower central series for Lie algebras is obtained.
KeywordsBaer's theorem, lower central series, nilpotent residual, upper central series, upper hypercenter, Z-decomposition
References: 
  1. Bahturin Yu.A. Identities in Lie algebras, Moscow: Nauka, 1985 (in Russian).
  2. Vaughan-Lee M.R. J. London Math. Soc., 1972, 5: 673–680. https://doi.org/10.1112/jlms/s2-5.4.673
  3. Stewart I.N. Compositio Math., 1970, 22: 313–331.
  4. Neumann B.H. Proc. London Math. Soc., 1951, 1: 178–187. https://doi.org/10.1112/plms/s3-1.1.178
  5. Baer R. Trans. Amer. Math. Soc., 1945, 58: 348–389. https://doi.org/10.1090/S0002-9947-1945-0015107-1
  6. Baer R. Math. Ann., 1952, 124: 161–177. https://doi.org/10.1007/BF01343558
  7. Wiegold J. Math. Z., 1965, 89: 345–347. https://doi.org/10.1007/BF01112166
  8. Hall P. Collected Works of Philip Hall, 1969: 415–462.
  9. Stewart I.N. Proc. London Math. Soc., 1974, 28: 129–140. https://doi.org/10.1112/plms/s3-28.1.129
  10. Stitzinger E., Turner R. Linear Multilinear Algebra, 1999, 45: 329–331. https://doi.org/10.1080/03081089908818596
  11. Saeedi F., Veisi B. Linear Multilinear Algebra, 2014, 62: 1139–1145. https://doi.org/10.1080/03081087.2013.809871
  12. Kurdachenko L.A., Otal J., Subbotin I.Ya. Proc. Amer. Math. Soc., 2013, 141: 2597–2602. https://doi.org/10.1090/S0002-9939-2013-11677-1