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

Zeitschrift:
Communications in Algebra

ISSN: 0092-7872

Datum der Publikation: 2009

Ausgabe: 37

Nummer: 10

Seiten: 3548-3552

Art: Artikel

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

Andere Publikationen in: Communications in Algebra

Projekte im Zusammenhang

Álgebras, triples y lazos relacionados con Geometría y Supersimetría

2007/00082/001

Zusammenfassung

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