The derived superalgebra of skew elements of a semiprime superalgebra with superinvolution

  1. Laliena, J. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Journal of Algebra

ISSN: 0021-8693

Year of publication: 2014

Volume: 420

Pages: 65-85

Type: Article

DOI: 10.1016/J.JALGEBRA.2014.07.031 SCOPUS: 2-s2.0-84908323461 WoS: WOS:000343020900005 GOOGLE SCHOLAR
Institutional repository: lock_openOpen access editor

Abstract

In this paper we investigate the Lie structure of the derived Lie superalgebra [K, K], with K the set of skew elements of a semiprime associative superalgebra A with superinvolution. We show that if U is a Lie ideal of [K, 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', A′, where the image of U in A' is central, and A′ is a subdirect product of orders in simple superalgebras, each at most 16-dimensional over its center.