Graded modules over classical simple Lie algebras with a grading

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.

38 pages

Cited by in corpus (5)

• Gradings on the Lie algebra $D_4$ revisited
• Gradings on the simple real Lie algebras of types $G_2$ and $D_4$
• Classification of irreducible bounded weight modules over the derivation Lie algebras of quantum tori
• Gradings on associative algebras with involution and real forms of classical simple Lie algebras
• Gradings on modules over Lie algebras of E types