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On primitive lie algebras

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Abstract

Sufficient conditions for Lie algebra primitiveness and examples of primitive Lie algebras and nonprimitive Lie algebras are given.

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References

  1. K. I. Beidar and S. A. Pikhtilkov, “The prime radical of the special Lie algebras,” Fundam. Prikl. Mat., 6, No. 3, 643–648 (2000).

    MathSciNet  MATH  Google Scholar 

  2. N. Bourbaki, Lie Groups and Algebras (Chapters I–III) [Russian translations], Mir, Moscow (1976).

    Google Scholar 

  3. J. Dixmier, Universal Enveloping Algebras [Russian translation], Mir, Moscow (1978).

    Google Scholar 

  4. I. Herstein, Non-Commutative Rings [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  5. N. Jacobson, Lie Algebras [Russian translation], Mir, Moscow (1964).

    Google Scholar 

  6. V. N. Latyshev, “On Lie algebras with polynomial identities,” Sib. Mat. Zh., 4, No. 4, 821–829 (1963).

    MATH  Google Scholar 

  7. S. A. Pikhtilkov, “The primitiveness of free associative algebra with finite number of generators,” Usp. Mat. Nauk, No. 1, 183–184 (1974).

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Authors and Affiliations

  1. Orenburg State University, Orenburg, Russia

    A. A. Kucherov, O. A. Pikhtilkova & S. A. Pikhtilkov

Authors
  1. A. A. Kucherov
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  2. O. A. Pikhtilkova
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  3. S. A. Pikhtilkov
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Corresponding authors

Correspondence to A. A. Kucherov or S. A. Pikhtilkov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 2, pp. 177–182, 2011/12.

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Kucherov, A.A., Pikhtilkova, O.A. & Pikhtilkov, S.A. On primitive lie algebras. J Math Sci 186, 651–654 (2012). https://doi.org/10.1007/s10958-012-1011-0

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  • DOI: https://doi.org/10.1007/s10958-012-1011-0

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