Bibliographic Details
| Title: |
Special pure gradings on simple Lie algebras of types E6, E7, E8. |
| Authors: |
Draper, Cristina1 (AUTHOR) cdf@uma.es, Elduque, Alberto1,2 (AUTHOR) elduque@unizar.es, Kochetov, Mikhail1,3 (AUTHOR) mikhail@mun.ca |
| Source: |
Linear Algebra & its Applications. May2026, Vol. 737, p263-297. 35p. |
| Subjects: |
Lie algebras, Quadratic forms, Weyl groups |
| 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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
