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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.53 supl.1 Bogotá Dec. 2019 Epub Mar 24, 2020
https://doi.org/10.15446/recolma.v53nsupl.84006
Artículos originales
Graded modules over simple Lie algebras
1 Memorial University of Newfoundland, Canada
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 
l2(ℂ), we consider specific gradings on simple modules of arbitrary dimension.
Keywords: graded Lie algebras; graded modules; simple modules; universal enveloping algebra
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 l2(ℂ), consideramos graduaciones específicas en módulos simples de dimensión arbitraria.
Palabras clave: Álgebras de Lie graduadas; módulos graduados; módulos simples; álgebra envolvente universal
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0The first author acknowledges support by the Discovery Grant 227060-14 of the Natural Sciences and Engineering Research Council (NSERC) of Canada. The second author acknowledges support by NSERC Discovery Grant 2018-04883. The third author acknowledges support by the Hashemite University of Jordan and NSERC of Canada.
Received: September 16, 2018; Accepted: February 11, 2019
Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons BY
