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 has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p › 5 a fi...

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1. Verfasser:	Strade, Helmut, 1942- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Berlin : Walter de Gruyter, [2017]
Ausgabe:	2nd edition.
Schriftenreihe:	De Gruyter expositions in mathematics ; 38.
Schlagworte:	Lie algebras. Algèbres de Lie. MATHEMATICS > Essays. MATHEMATICS > Pre-Calculus. MATHEMATICS > Reference. Lie algebras Lie algebras, fields of positive characteristic, structure theory.
Online-Zugang:	Volltext
Zusammenfassung:	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 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 simple 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. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. The concise presentation of the general theory underlying the subject matter and the presentation of classification results on a subclass of the simple Lie algebras for all odd primes will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. Contents Toral subalgebras in p-envelopesLie algebras of special derivationsDerivation simple algebras and modulesSimple Lie algebrasRecognition theoremsThe isomorphism problemStructure of simple Lie algebrasPairings of induced modulesToral rank 1 Lie algebras.
Beschreibung:	1 online resource
ISBN:	9783110515237 3110515237 311051544X 9783110515442