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Lie identities on symmetric elements of restricted enveloping algebras

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Abstract

Let L be a restricted Lie algebra over a field of characteristic p > 2 and denote by u(L) its restricted enveloping algebra. We determine the conditions under which the set of symmetric elements of u(L) with respect to the principal involution is Lie solvable, Lie nilpotent, or bounded Lie Engel.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Via Provinciale Lecce-Arnesano, 73100, Lecce, Italy

    Salvatore Siciliano

  2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, Canada, A1C 5S7

    Hamid Usefi

Authors
  1. Salvatore Siciliano
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  2. Hamid Usefi
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Correspondence to Salvatore Siciliano.

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Supported by NSERC and MITACS.

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Siciliano, S., Usefi, H. Lie identities on symmetric elements of restricted enveloping algebras. Isr. J. Math. 195, 999–1012 (2013). https://doi.org/10.1007/s11856-012-0144-7

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  • DOI: https://doi.org/10.1007/s11856-012-0144-7

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