Strade Classifying the Absolute Toral Rank Two Case

1. Auflage 2008
ISBN: 978-3-11-020305-9
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 391 Seiten

Reihe: ISSN

The problem of classifying the finite-dimensional simple Lie algebras over fields of characteristic > 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 5. This conjecture was proved for > 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 > 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: 3

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.

Zielgruppe

Researchers, Lecturers, Graduates, and Advanced in Algebra; Acade

Autoren/Hrsg.

Strade, Helmut

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Frontmatter
Contents
Introduction
Chapter 10. Tori in Hamiltonian and Melikian algebras
Chapter 11. 1-sections
Chapter 12. Sandwich elements and rigid tori
Chapter 13. Towards graded algebras
Chapter 14. The toral rank 2 case
Chapter 15. Supplements to Volume 1
Backmatter

Über Autor(innen)

Strade, Helmut
Helmut Strade, University of Hamburg, Germany.

Helmut Strade, Universitty of Hamburg, Germany.