Gradings on modules over Lie algebras of E types

Abstract

For any grading by an abelian group $G$ on the exceptional simple Lie algebra $\mathcal{L}$ of type $E_6$ or $E_7$ over an algebraically closed field of characteristic zero, we compute the graded Brauer invariants of simple finite-dimensional modules, thus completing the computation of these invariants for simple finite-dimensional Lie algebras. This yields the classification of $G$-graded simple $\mathcal{L}$-modules, as well as necessary and sufficient conditions for an $\mathcal{L}$-module to admit a $G$-grading compatible with the given $G$-grading on $\mathcal{L}$.

21 pages

References in corpus (2)

• Graded modules over classical simple Lie algebras with a grading
• Gradings on the Lie algebra $D_4$ revisited

Cited by in corpus (1)

• Linear models of the exceptional Lie algebra ${\mathfrak{e}}_8$