Graded modules over simple Lie algebras

• Bahturin, Yuri ^[1] ; Kochetov, Mikhail ^[1] ; Shihadeh, Abdallah ^[1]
  1. [1] Memorial University of Newfoundland

     Memorial University of Newfoundland

     Canadá

     
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 53, Nº. Extra 1, 2019 (Ejemplar dedicado a: Suplemento), págs. 45-86
• Idioma: inglés
• DOI: 10.15446/recolma.v53nsupl.84006
• Enlaces
  • Texto completo
• Resumen
  • español

    El artículo está dedicado al estudio de módulos graduados simples y graduaciones de módulos simples sobre álgebras de Lie simples de dimensión finita. En general, una conexión entre estos dos objetos viene dada por la llamada construcción de lazos. Revisaremos las características principales de esta construcción, así como las condiciones necesarias y suficientes bajo las cuales se pueden graduar los módulos simples de dimensión finita. Para el álgebra de Lie sl2(C), consideramos graduaciones específicas en módulos simples de dimensión arbitraria.

  • English

    The paper is devoted to the study of graded-simple modules and gradings on simple modules over finite-dimensional simple Lie algebras. In general, a connection between these two objects is given by the so-called loop construction. We review the main features of this construction as well as necessary and sufficient conditions under which finite-dimensional simple modules can be graded. Over the Lie algebra sl2(C), we consider specific gradings on simple modules of arbitrary dimension.

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