Special pure gradings on simple Lie algebras of types E6, E7, E8.
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| Title: | Special pure gradings on simple Lie algebras of types E6, E7, E8. |
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| 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] |
| Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 192196636 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Special pure gradings on simple Lie algebras of types E6, E7, E8. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Draper%2C+Cristina%22">Draper, Cristina</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> cdf@uma.es</i><br /><searchLink fieldCode="AR" term="%22Elduque%2C+Alberto%22">Elduque, Alberto</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> elduque@unizar.es</i><br /><searchLink fieldCode="AR" term="%22Kochetov%2C+Mikhail%22">Kochetov, Mikhail</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> mikhail@mun.ca</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. May2026, Vol. 737, p263-297. 35p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Lie+algebras%22">Lie algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Quadratic+forms%22">Quadratic forms</searchLink><br /><searchLink fieldCode="DE" term="%22Weyl+groups%22">Weyl groups</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=192196636 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.laa.2026.02.019 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 35 StartPage: 263 Subjects: – SubjectFull: Lie algebras Type: general – SubjectFull: Quadratic forms Type: general – SubjectFull: Weyl groups Type: general Titles: – TitleFull: Special pure gradings on simple Lie algebras of types E6, E7, E8. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Draper, Cristina – PersonEntity: Name: NameFull: Elduque, Alberto – PersonEntity: Name: NameFull: Kochetov, Mikhail IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00243795 Numbering: – Type: volume Value: 737 Titles: – TitleFull: Linear Algebra & its Applications Type: main |
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