Special pure gradings on simple Lie algebras of types E6, E7, E8
Abstract
A group grading on a semisimple Lie algebra over an algebraically closed field of characteristic zero is special if its identity component is zero; it is pure if at least one of its components, other than the identity component, contains a Cartan subalgebra. We classify special pure gradings on Lie algebras of types $E_6$, $E_7$, $E_8$ up to equivalence and up to isomorphism. To this end, we use quadratic forms over the field of two elements to show that there are exactly three equivalence classes for $E_6$, four for $E_7$, and five for $E_8$. The computation of the corresponding Weyl groups and their actions on the universal groups yields a set of invariants that allow us to distinguish the isomorphism classes.
Fields of Study & Subjects
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Linear Algebra and its Applications
- Publisher
- Elsevier BV
- Volume
- 737
- Pages
- 263–297
- Publication date
- 23 February 2026
- Language
- EN