Ukrainian Mathematical Journal

, Volume 70, Issue 7, pp 1141–1144 | Cite as

A Note on Strongly Split Lie Algebras

  • A. J. Calderón Martín

Split Lie algebras are possibly the most known examples of graded Lie algebras. Since an important category in the class of graded algebras is the category of strongly graded algebras, we introduce, in a natural way, the category of strongly split Lie algebras 𝔏 and show that if 𝔏 is centerless, then 𝔏 is the direct sum of split ideals each of which is a split-simple strongly split Lie algebra.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. J. Calderón, “On split Lie algebras with symmetric root systems,” Proc. Indian Acad. Sci. Math. Sci., 118, 351–356 (2008).MathSciNetCrossRefGoogle Scholar
  2. 2.
    M. Kochetov, “Gradings on finite-dimensional simple Lie algebras,” Acta Appl. Math., 108, No. 1, 101–127 (2009).MathSciNetCrossRefGoogle Scholar
  3. 3.
    C. Nastasescu and F. Van Oystaeyen, “Methods of graded rings,” Lect. Notes Math., 1836, Springer-Verlag, Berlin (2004).Google Scholar
  4. 4.
    K.-H. Neeb, “Integrable roots in split graded Lie algebras,” J. Algebra, 225, No. 2, 534–580 (2000).MathSciNetCrossRefGoogle Scholar
  5. 5.
    J. R. Schue, “Hilbert space methods in the theory of Lie algebras,” Trans. Amer. Math. Soc., 95, 69–80 (1960).MathSciNetCrossRefGoogle Scholar
  6. 6.
    N. Stumme, “The structure of locally finite split Lie algebras,” J. Algebra, 220, 664–693 (1999).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • A. J. Calderón Martín
    • 1
  1. 1.University of CádizCádizSpain

Personalised recommendations