Completion of the Classification (De Gruyter Expositions in Mathematics, 57, Band 3) - Hardcover

Strade, Helmut

Hardcover

ISBN 10: 3110262983 ISBN 13: 9783110262988

Verlag: De Gruyter, 2012

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

Helmut Strade, University of Hamburg, Germany.

Von der hinteren Coverseite

This is the third part of a three-volume book about the classification of the simple Lie algebras over algebraically closed fields of characteristic > 3. The first volume contains the methods, examples and a first classification result, while in the second volume the proof for the case of absolute toral rank 2 simple Lie algebras is completed. Based on these results the present third volume completes the Classification proof for the general case. One of the very important intermediate results is the decision when elements act nilpotently on the whole algebra. This result then allows to describe 2-sections with respect to a torus of maximal dimension in a minimal p-envelope. Different methods apply for the cases that such a torus exists which is non-standard (giving the Melikian algebras), such a torus exists which has only solvable roots (giving some Special algebras and some Block algebras), no torus of maximal dimension of these two types exists (giving the classical and most of the Cartan type algebras).

Details zur Ausgabe

• Verlag: De Gruyter
• Erscheinungsdatum: 2012
• Sprache: Englisch
• ISBN 10: 3110262983
• ISBN 13: 9783110262988
• Einband: Gebundene Ausgabe
• Auflage: 1
• Anzahl der Seiten: 249
• Kontakt zum Hersteller: productsafety@degruyterbrill.com; productsafety@degruyterbrill.com; ; Theaterstraße 13; Göttingen; 37073; Deutschland