Strade Structure Theory

Nachdruck 2014
ISBN: 978-3-11-019794-5
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 38, 548 Seiten, Format (B × H): 155 mm x 230 mm, Gewicht: 10 g

Reihe: De Gruyter Expositions in MathematicsISSN

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 first volume is devoted to preparing the ground for the classification work to be performed in the second and third volume. 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 make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in albegra.

Zielgruppe

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

Autoren/Hrsg.

Strade, Helmut

Fachgebiete

• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

1;Frontmatter;1
2;Contents;7
3;Introduction;9
4;Chapter 1. Toral subalgebras in p-envelopes;25
5;Chapter 2. Lie algebras of special derivations;66
6;Chapter 3. Derivation simple algebras and modules;141
7;Chapter 4. Simple Lie algebras;188
8;Chapter 5. Recognition theorems;225
9;Chapter 6. The isomorphism problem;291
10;Chapter 7. Structure of simple Lie algebras;365
11;Chapter 8. Pairings of induced modules;440
12;Chapter 9. Toral rank 1 Lie algebras;492
13;Backmatter;529

Über Autor(innen)

Helmut Strade, University of Hamburg, Germany.