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Siberian Mathematical Journal

, Volume 54, Issue 3, pp 472–478 | Cite as

Lie and Engel theorems for n-tuple lie algebras

  • N. A. KoreshkovEmail author
Article

Abstract

We prove some analogs of the Lie and Engel theorems for n-tuple Lie algebras. Furthermore, we establish existence of Cartan subalgebras in the n-tuple Lie algebras.

Keywords

n-tuple Lie algebra 

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References

  1. 1.
    Koreshkov N. A., “Nilpotency of n-tuple Lie algebras and associative n-tuple algebras,” Russian Math. (Izv. VUZ. Matematika), 54, No. 2, 28–32 (2010).MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Dotsenko V. V. and Khoroshkin A. S., “Formulas of an operad character of a pair of coordinated parentheses and a bi-Hamiltonian operad,” Funct. Anal. Appl., 41, No. 1, 1–17 (2007).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Humphreys J. E., Introduction to Lie Algebras and Representation Theory, Springer-Verlag, New York, Heidelberg, and Berlin (1980).zbMATHGoogle Scholar
  4. 4.
    Koreshkov N. A., “Triangulation of n-tuple solvable Lie algebras,” Russian Math. (Izv. VUZ. Matematika), 56, No. 2, 56–59 (2012).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Jacobson N., Lie Algebras, Wiley and Sons, New York etc. (1962).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazanRussia

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