Journal of Mathematical Sciences

, Volume 197, Issue 4, pp 558–564 | Cite as

New Properties of the Lie Algebra Variety N2A

  • S. P. Mishchenko
  • Y. R. Fyathutdinova


We continue to consider the properties of the almost polynomial growth variety of Lie algebras over a field of characteristic zero defined by the identity (x 1 x 2)(x 3 x 4)(x 5 x 6) ≡ 0. Here we have constructed the bases of its multilinear parts and proved the formulas for the colength and codimension sequences of this variety.


Irreducible Character Polynomial Growth Free Algebra Identical Relation Irreducible Module 
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  1. 1.
    Yu. Bahturin, Identical Relations in Lie Algebras, VNU Sci. Press, Utrecht (1987).MATHGoogle Scholar
  2. 2.
    A. Giambruno and M. Zaicev, Polynomial Identities and Asymptotic Methods, Math. Surveys Monographs, Vol. 122, Amer. Math. Soc., Providence (2005).Google Scholar
  3. 3.
    A. I. Maltsev, “On algebras with identical constitutive relations,” Mat. Sb., 26, No. 1, 19–33 (1950).Google Scholar
  4. 4.
    S. P. Mishenko, “Varieties of Lie algebras with the bidegree nilpotent commutant,” Vestsi Akad. Navuk BSSR. Ser. Fiz.-Mat. Navuk, No. 6, 39–43 (1987).Google Scholar
  5. 5.
    S. P. Mishchenko, “Growth of varieties of Lie algebras,” Russ. Math. Surv., 45, No. 6, 27–52 (1990).CrossRefMATHMathSciNetGoogle Scholar

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Algebra and Geometric ComputationsUlyanovsk State UniversityUlyanovskRussia

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