2026-06-06T19:32:12Zhttps://riuma.uma.es/rest/oai/request

oai:riuma.uma.es:10630/464822026-04-28T23:45:37Zcom_10630_2254col_10630_37953

00925njm 22002777a 4500 dc Kochetov, Mikhail author Elduque, Alberto author Draper-Fontanals, Cristina author 2026-02-26 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 E6, E7, E8 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 E6, four for E7, and five for E8. 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. Cristina Draper, Alberto Elduque, Mikhail Kochetov, Special pure gradings on simple Lie algebras of types E6, E7, E8, Linear Algebra and its Applications, Volume 737, 2026, Pages 263-297, ISSN 0024-3795, https://doi.org/10.1016/j.laa.2026.02.019. (https://www.sciencedirect.com/science/article/pii/S0024379526000704) https://hdl.handle.net/10630/46482 10.1016/j.laa.2026.02.019 Álgebra abstracta Lie, Álgebras de Análisis matemático Special pure gradings on simple Lie algebras of types $E_6$, $E_7$, $E_8$.