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arXiv · 1308.6089

Graded modules over classical simple Lie algebras with a grading

Alberto Elduque·Mikhail Kochetov
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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 D4, 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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BibTeXRIS

Alberto Elduque, Mikhail Kochetov. 2015-07-21. Graded modules over classical simple Lie algebras with a grading. https://doi.org/10.1007/s11856-015-1174-8

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