Lie structure in semiprime superalgebras with superinvolution

  1. Laliena, J. 1
  2. Sacristán, S. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Journal of Algebra

ISSN: 0021-8693

Ano de publicación: 2007

Volume: 315

Número: 2

Páxinas: 751-760

Tipo: Artigo

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DOI: 10.1016/J.JALGEBRA.2007.04.005 SCOPUS: 2-s2.0-34547966084 WoS: WOS:000249556500019 GOOGLE SCHOLAR lock_openAcceso aberto editor

Outras publicacións en: Journal of Algebra

Repositorio institucional: lock_openAcceso aberto Editor

Resumo

In this paper we investigate the Lie structure of the Lie superalgebra K of skew elements of a semiprime associative superalgebra A with superinvolution. We show that if U is a Lie ideal of K, then either there exists an ideal J of A such that the Lie ideal [J ∩ K, K] is nonzero and contained in U, or A is a subdirect sum of A<sup>′</sup>, A<sup>″</sup>, where the image of U in A<sup>′</sup> is central, and A<sup>″</sup> is a subdirect product of orders in simple superalgebras, each at most 16-dimensional over its center. © 2007 Elsevier Inc. All rights reserved.