Simple Lie Algebras Over Fields of Positive Characteristic: Classifying the absolute toral rank two case

Simple Lie Algebras Over Fields of Positive Characteristic: Classifying the absolute toral rank two case
Author :
Publisher : Walter de Gruyter
Total Pages : 392
Release :
ISBN-10 : 9783110197013
ISBN-13 : 3110197014
Rating : 4/5 (014 Downloads)

Book Synopsis Simple Lie Algebras Over Fields of Positive Characteristic: Classifying the absolute toral rank two case by : Helmut Strade

Download or read book Simple Lie Algebras Over Fields of Positive Characteristic: Classifying the absolute toral rank two case written by Helmut Strade and published by Walter de Gruyter. This book was released on 2004 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Simple Lie Algebras Over Fields of Positive Characteristic: Classifying the absolute toral rank two case Related Books

Simple Lie Algebras Over Fields of Positive Characteristic: Classifying the absolute toral rank two case
Language: en
Pages: 392
Authors: Helmut Strade
Categories: Mathematics
Type: BOOK - Published: 2004 - Publisher: Walter de Gruyter

GET EBOOK

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 t
Classifying the Absolute Toral Rank Two Case
Language: en
Pages: 394
Authors: Helmut Strade
Categories: Mathematics
Type: BOOK - Published: 2017-04-10 - Publisher: Walter de Gruyter GmbH & Co KG

GET EBOOK

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
Simple Lie Algebras Over Fields of Positive Characteristic: Structure theory
Language: en
Pages: 548
Authors: Helmut Strade
Categories: Mathematics
Type: BOOK - Published: 2004 - Publisher: Walter de Gruyter

GET EBOOK

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 t
Gradings on Simple Lie Algebras
Language: en
Pages: 355
Authors: Alberto Elduque
Categories: Mathematics
Type: BOOK - Published: 2013 - Publisher: American Mathematical Soc.

GET EBOOK

This monograph is a self-contained exposition of the classification of gradings by arbitrary groups on classical simple Lie algebras over algebraically closed f
Lie Algebras and Related Topics
Language: en
Pages: 258
Authors: Marina Avitabile
Categories: Mathematics
Type: BOOK - Published: 2015-11-30 - Publisher: American Mathematical Soc.

GET EBOOK

This volume contains the proceedings of the Workshop on Lie Algebras, in honor of Helmut Strade's 70th Birthday, held from May 22-24, 2013, at the Università d