Counting gradings on Lie algebras of block-triangular matrices.
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| Title: | Counting gradings on Lie algebras of block-triangular matrices. |
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| Authors: | Diniz, Diogo1 (AUTHOR) diogo@mat.ufcg.edu.br, Borges, Alex Ramos2 (AUTHOR) alex.borges@upe.br, Fonsêca, Eduardo1 (AUTHOR) eduardo@mat.ufcg.edu.br |
| Source: | Linear Algebra & its Applications. Dec2024, Vol. 703, p504-527. 24p. |
| Subjects: | Lie algebras, Isomorphism (Mathematics), Matrices (Mathematics), Finite groups, Number theory, Abelian groups |
| Abstract: | We study the number of isomorphism classes of gradings on Lie algebras of block-triangular matrices. Let G be a finite abelian group, for m ∈ N s we determine the number E (−) (G , m) of isomorphism classes of elementary G -gradings on the Lie algebra U T (m) (−) of block-triangular matrices over an algebraically closed field of characteristic zero. We study the asymptotic growth of E (−) (G , m) and as a consequence prove that the E (−) (G , ⋅) determines G up to isomorphism. We also study the asymptotic growth of the number N (−) (G , m) of isomorphism classes of G -gradings on U T (m) (−) and prove that N (−) (G , m)) ∼ | G | E (−) (G , m). [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: 180423474 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Counting gradings on Lie algebras of block-triangular matrices. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Diniz%2C+Diogo%22">Diniz, Diogo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> diogo@mat.ufcg.edu.br</i><br /><searchLink fieldCode="AR" term="%22Borges%2C+Alex+Ramos%22">Borges, Alex Ramos</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> alex.borges@upe.br</i><br /><searchLink fieldCode="AR" term="%22Fonsêca%2C+Eduardo%22">Fonsêca, Eduardo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> eduardo@mat.ufcg.edu.br</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. Dec2024, Vol. 703, p504-527. 24p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Lie+algebras%22">Lie algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Isomorphism+%28Mathematics%29%22">Isomorphism (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+groups%22">Finite groups</searchLink><br /><searchLink fieldCode="DE" term="%22Number+theory%22">Number theory</searchLink><br /><searchLink fieldCode="DE" term="%22Abelian+groups%22">Abelian groups</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We study the number of isomorphism classes of gradings on Lie algebras of block-triangular matrices. Let G be a finite abelian group, for m ∈ N s we determine the number E (−) (G , m) of isomorphism classes of elementary G -gradings on the Lie algebra U T (m) (−) of block-triangular matrices over an algebraically closed field of characteristic zero. We study the asymptotic growth of E (−) (G , m) and as a consequence prove that the E (−) (G , ⋅) determines G up to isomorphism. We also study the asymptotic growth of the number N (−) (G , m) of isomorphism classes of G -gradings on U T (m) (−) and prove that N (−) (G , m)) ∼ | G | E (−) (G , m). [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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.laa.2024.10.002 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: 504 Subjects: – SubjectFull: Lie algebras Type: general – SubjectFull: Isomorphism (Mathematics) Type: general – SubjectFull: Matrices (Mathematics) Type: general – SubjectFull: Finite groups Type: general – SubjectFull: Number theory Type: general – SubjectFull: Abelian groups Type: general Titles: – TitleFull: Counting gradings on Lie algebras of block-triangular matrices. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Diniz, Diogo – PersonEntity: Name: NameFull: Borges, Alex Ramos – PersonEntity: Name: NameFull: Fonsêca, Eduardo IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 12 Text: Dec2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 00243795 Numbering: – Type: volume Value: 703 Titles: – TitleFull: Linear Algebra & its Applications Type: main |
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