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On Description of Leibniz Algebras Corresponding to sl 2

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Abstract

In this paper we describe finite-dimensional complex Leibniz algebras whose quotient algebra with respect to the ideal I generated by squares is isomorphic to the simple Lie algebra sl 2. It is shown that the number of isomorphism classes such of Leibniz algebras coincides with the number of partitions of dim I.

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Authors and Affiliations

  1. Institute of Mathematics and Information Technologies, Uzbekistan Academy of Science, F. Hodjaev Str. 29, 100125, Tashkent, Uzbekistan

    B. A. Omirov & I. S. Rakhimov

  2. Institute for Mathematical Research (INSPEM) and Department of Mathematics, FS, Universiti Putra Malaysia, 43400, UPM, Serdang, Selangor Darul Ehsan, Malaysia

    I. S. Rakhimov

  3. Department of Mathematics, National University of Uzbekistan, Vuzgorogok, 27, 100174, Tashkent, Uzbekistan

    R. M. Turdibaev

Authors
  1. B. A. Omirov
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  2. I. S. Rakhimov
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  3. R. M. Turdibaev
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Correspondence to I. S. Rakhimov.

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Omirov, B.A., Rakhimov, I.S. & Turdibaev, R.M. On Description of Leibniz Algebras Corresponding to sl 2 . Algebr Represent Theor 16, 1507–1519 (2013). https://doi.org/10.1007/s10468-012-9367-x

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  • DOI: https://doi.org/10.1007/s10468-012-9367-x

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