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
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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.