Completion of the Classification
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| Title: | Completion of the Classification |
|---|---|
| Description: | The problem of classifying the finite-dimensional simple Lie algebras over fields of characteristic p > 0 is a long-standing one. Work on this question during the last 45 years has been directed by the Kostrikin–Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite-dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin–Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block–Wilson–Strade–Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every finite-dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic leading to the forefront of current research in this field. This is the last of three volumes. In this monograph the proof of the Classification Theorem presented in the first volume is concluded. It collects all the important results on the topic which can be found only in scattered scientific literature so far. |
| Authors: | Helmut Strade |
| Resource Type: | eBook. |
| Subjects: | Lie algebras |
| Categories: | MATHEMATICS / Algebra / General |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf Text: Availability: 0 |
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| Header | DbId: nlebk DbLabel: eBook Collection (EBSCOhost) An: 544006 RelevancyScore: 1051 AccessLevel: 6 PubType: eBook PubTypeId: ebook PreciseRelevancyScore: 1050.81640625 |
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| Items | – Name: Title Label: Title Group: Ti Data: Completion of the Classification – Name: Abstract Label: Description Group: Ab Data: The problem of classifying the finite-dimensional simple Lie algebras over fields of characteristic p > 0 is a long-standing one. Work on this question during the last 45 years has been directed by the Kostrikin–Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite-dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin–Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block–Wilson–Strade–Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every finite-dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. In the three-volume book, the author is assembling the proof of the Classification Theorem with explanations and references. The goal is a state-of-the-art account on the structure and classification theory of Lie algebras over fields of positive characteristic leading to the forefront of current research in this field. This is the last of three volumes. In this monograph the proof of the Classification Theorem presented in the first volume is concluded. It collects all the important results on the topic which can be found only in scattered scientific literature so far. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Helmut+Strade%22">Helmut Strade</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Lie+algebras%22">Lie algebras</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Algebra+%2F+General%22">MATHEMATICS / Algebra / General</searchLink> |
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| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 512.55 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Lie algebras Type: general Titles: – TitleFull: Completion of the Classification Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Helmut Strade – PersonEntity: Name: NameFull: Helmut Strade IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2013 – D: 04 M: 02 Type: profile Y: 2014 Identifiers: – Type: isbn-print Value: 9783110262988 – Type: isbn-electronic Value: 9783110263015 Numbering: – Type: volume Value: III Titles: – TitleFull: Completion of the Classification Type: main |
| ResultId | 1 |
