Classifying the Absolute Toral Rank Two Case

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Title:	Classifying the Absolute Toral Rank Two Case
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 second part of the three-volume book about the classification of the simple Lie algebras over algebraically closed fields of characteristics > 3. The first volume contains the methods, examples, and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to Aleksei. I. Kostrikin and Alexander A. Premet and the investigation of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristics > 3 is given.
Authors:	Helmut Strade
Resource Type:	eBook.
Subjects:	Lie algebras, Algebra
Categories:	MATHEMATICS / Algebra / General
Database:	eBook Collection (EBSCOhost)

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Items	– Name: Title Label: Title Group: Ti Data: Classifying the Absolute Toral Rank Two Case – 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 second part of the three-volume book about the classification of the simple Lie algebras over algebraically closed fields of characteristics > 3. The first volume contains the methods, examples, and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to Aleksei. I. Kostrikin and Alexander A. Premet and the investigation of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristics > 3 is given. – 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><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</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 – SubjectFull: Algebra Type: general Titles: – TitleFull: Classifying the Absolute Toral Rank Two Case Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Helmut Strade – PersonEntity: Name: NameFull: Helmut Strade IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2009 – D: 04 M: 02 Type: profile Y: 2014 Identifiers: – Type: isbn-print Value: 9783110197013 – Type: isbn-electronic Value: 9783110203059 Numbering: – Type: volume Value: II Titles: – TitleFull: Classifying the Absolute Toral Rank Two Case Type: main
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