Finite dimensional compact and unitary Lie superalgebras

• Saeid Azam ^[1] ; Karl-Hermann Neeb ^[2]
  1. [1] Institute for Research in Fundamental Sciences

     Institute for Research in Fundamental Sciences

     Irán

     
  2. [2] Friedrich-Alexander University Erlangen–Nuremberg, Germany
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 10 (October 2015), 2015, págs. 4422-4440
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.02.024
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• Resumen

  • Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is achieved by describing the classification of real finite dimensional compact simple Lie superalgebras, and analyzing, in a rather elementary and direct way, the decomposition of reductive Lie superalgebras (g is a semisimple -module) over fields of characteristic zero into ideals.