000169993 001__ 169993 000169993 005__ 20260316092629.0 000169993 0247_ $$2doi$$a10.1016/j.laa.2026.02.019 000169993 0248_ $$2sideral$$a148523 000169993 037__ $$aART-2026-148523 000169993 041__ $$aeng 000169993 100__ $$aDraper, Cristina 000169993 245__ $$aSpecial pure gradings on simple Lie algebras of types E6, E7, E8 000169993 260__ $$c2026 000169993 5060_ $$aAccess copy available to the general public$$fUnrestricted 000169993 5203_ $$aA 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. 000169993 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E22-20R$$9info:eu-repo/grantAgreement/ES/MCINN/PID2021-123461NB-C21 000169993 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es 000169993 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000169993 700__ $$0(orcid)0000-0002-6497-2162$$aElduque, Alberto$$uUniversidad de Zaragoza 000169993 700__ $$aKochetov, Mikhail 000169993 7102_ $$12006$$2005$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Algebra 000169993 773__ $$g737 (2026), 263-297$$pLinear algebra appl.$$tLINEAR ALGEBRA AND ITS APPLICATIONS$$x0024-3795 000169993 8564_ $$s1430292$$uhttps://zaguan.unizar.es/record/169993/files/texto_completo.pdf$$yVersión publicada 000169993 8564_ $$s1557048$$uhttps://zaguan.unizar.es/record/169993/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000169993 909CO $$ooai:zaguan.unizar.es:169993$$particulos$$pdriver 000169993 951__ $$a2026-03-16-08:16:26 000169993 980__ $$aARTICLE