On Certain Semiprime Associative Superalgebras

  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

Journal:
Communications in Algebra

ISSN: 0092-7872

Year of publication: 2009

Volume: 37

Issue: 10

Pages: 3548-3552

Type: Article

DOI: 10.1080/00927870902828470 SCOPUS: 2-s2.0-70449492581 WoS: WOS:000273643000014 GOOGLE SCHOLAR

More publications in: Communications in Algebra

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Abstract

In this note we emphasise the relationship between the structure of an associative superalgebra with superinvolution and the structure of the Lie substructure of skewsymmetric elements. More explicitly, we show that if A is a semiprime associative superalgebra with superinvolution and K is the Lie superalgebra of skewsymmetric elements satisfying [K<sup>2</sup>, K<sup>2</sup>] = 0, then A is a subdirect product of orders in simple superalgebras each at most 4-dimensional over its center