Simple lie algebras over fields of positive characteristic III, completion of the classification / by Helmut Strade.

Format:

Book

Author/Creator:

Strade, Helmut.

Series:

De Gruyter Expositions in Mathematics

De Gruyter expositions in mathematics, 0938-6572 ; 57

De Gruyter Expositions in Mathematics ; 57

Language:

English

Subjects (All):

Lie algebras.

Physical Description:

1 online resource (249 p.)

Edition:

1st ed.

Place of Publication:

Berlin : De Gruyter, 2013.

Language Note:

English

Summary:

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.

Contents:

Front matter

Contents

Introduction

Chapter 16. Miscellaneous

Chapter 17. Sections

Chapter 18. Solving the case when T is non-standard

Chapter 19. Solving the case when all T-roots are solvable

Chapter 20. Attacking the general case

Notation

Bibliography

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

3-11-026301-7

OCLC:

829462266