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Siberian Mathematical Journal

, Volume 25, Issue 3, pp 370–382 | Cite as

Varieties of Lie algebras with the identity [[X1, X2, X3], [X4, X5, X6]]=0 over a field of characteristic zero

  • I. B. Volichenko
Article

Keywords

Characteristic Zero 
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Literature Cited

  1. 1.
    Yu. P. Razmyslov, “Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero,” Algebra Logika,12, No. 1, 83–113 (1973).Google Scholar
  2. 2.
    G. Higman, “Ordering by divisibility in abstract algebras,” Proc. London Math. Soc.,2, No. 2, 326–336 (1952).Google Scholar
  3. 3.
    M. R. Vaughan-Lee, “Abelian-by-nilpotent varieties of Lie algebras,” J. London Math. Soc.,11, No. 3, 263–266 (1975).Google Scholar
  4. 4.
    S. A. Amitsur, “The identities of PI-rings,” Proc. Am. Math. Soc.,4, No. 1, 27–34 (1953).Google Scholar
  5. 5.
    A. Regev, “The representations of Sn and explicit identities for PI-algebras,” J. Algebra,51, 25–40 (1978).Google Scholar
  6. 6.
    A. Regev, “Existence of polynomial identities in A ⊗ B” Bull. Am. Math. Soc.,77, No. 6, 1067–1069 (1971).Google Scholar
  7. 7.
    V. N. Latyshev, “Regev's theorem on identities in the tensor product of PI-algebras,” Usp. Mat. Nauk,27, No. 4, 213–214 (1972).Google Scholar
  8. 8.
    I. B. Volichenko, “Bases of a free Lie algebra modulo certain T-ideals,” Dokl. Akad. Nauk BSSR,24, No. 5, 400–403 (1980).Google Scholar
  9. 9.
    I. B. Volichenko, “Varieties of representations of Lie algebras,” in: Proceedings of the 16th All-Union Algebra Conference, Part 1, Leningrad (1981), p. 32.Google Scholar
  10. 10.
    G. de B. Robinson, Representation Theory of the Symmetric Group, University of Toronto Press, Toronto (1961).Google Scholar
  11. 11.
    C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience, New York, London (1952).Google Scholar
  12. 12.
    V. N. Latyshev, “On the choice of basis in a T-ideal,” Sib. Mat. Zh.,4, No. 5, 1122–1127 (1963).Google Scholar
  13. 13.
    J.-P. Serre, Linear Representations of Finite Groups, Springer-Verlag, New York-Heidelberg-Berlin (1970).Google Scholar
  14. 14.
    L. A. Bokut', “A basis for free polynilpotent Lie algebras,” Algebra Logika,2, No. 4, 13–20 (1963).Google Scholar
  15. 15.
    V. N. Latyshev, “The Spechtianness of certain varieties of associative algebras,” Algebra Logika,8, No. 6, 600–673 (1969).Google Scholar

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© Plenum Publishing Corporation 1985

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  • I. B. Volichenko

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