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Centralizers in Lie Algebras

Author

Listed:
  • Somayeh Saffarnia

    (Ferdowsi University of Mashhad)

  • Mohammad Reza R. Moghaddam

    (Khayyam University
    Ferdowsi University of Mashhad)

  • Mohammad Amin Rostamyari

    (Khayyam University)

Abstract

We determine the number of centralizers of different non-abelian finite dimensional Lie algebras over a specific field. Also, the concept of Lie algebras with abelian centralizers are studied and using a result of Bokut and Kukin [5], for a given residually free Lie algebra L, it is shown that L is fully residually free if and only if every centralizer of non-zero elements of L is abelian.

Suggested Citation

  • Somayeh Saffarnia & Mohammad Reza R. Moghaddam & Mohammad Amin Rostamyari, 2018. "Centralizers in Lie Algebras," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(1), pages 39-49, March.
    • Handle: RePEc:spr:indpam:v:49:y:2018:i:1:d:10.1007_s13226-018-0252-0
    DOI: 10.1007/s13226-018-0252-0
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    Cited by:

    1. Pratulananda Das & Ripan Saha, 2020. "On Leibniz Algebras Whose Centralizers Are Ideals," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1555-1571, December.

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