Abstract
Given a grading by an abelian group G on a semisimple Lie algebra L over an algebraically closed field of characteristic 0, we classify up to isomorphism the simple objects in the category of finite-dimensional G-graded L-modules. The invariants appearing in this classification are computed in the case when L is simple classical (except for type D 4, where a partial result is given). In particular, we obtain criteria to determine when a finite-dimensional simple L-module admits a G-grading making it a graded L-module.
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Supported by the Spanish Ministerio de Economía y Competitividad—Fondo Europeo de Desarrollo Regional (FEDER) MTM2010-18370-C04-02 and by the Diputación General de Aragón—Fondo Social Europeo (Grupo de Investigación de Álgebra).
Supported by a sabbatical research grant of Memorial University and a grant for visiting scientists by Instituto Universitario de Matemáticas y Aplicaciones, University of Zaragoza.
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Elduque, A., Kochetov, M. Graded modules over classical simple Lie algebras with a grading. Isr. J. Math. 207, 229–280 (2015). https://doi.org/10.1007/s11856-015-1174-8
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DOI: https://doi.org/10.1007/s11856-015-1174-8