UID:
almahu_9949462248702882
Format:
1 online resource (385 p.)
ISBN:
9783110203059
,
9783110494969
Series Statement:
De Gruyter Expositions in Mathematics , 42
Content:
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.
Note:
Frontmatter --
,
Contents --
,
Introduction --
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Chapter 10. Tori in Hamiltonian and Melikian algebras --
,
Chapter 11. 1-sections --
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Chapter 12. Sandwich elements and rigid tori --
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Chapter 13. Towards graded algebras --
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Chapter 14. The toral rank 2 case --
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Chapter 15. Supplements to Volume 1 --
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Backmatter
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Issued also in print.
,
Mode of access: Internet via World Wide Web.
,
In English.
In:
DG Expositions in Mathematics Backlist eBook Package, De Gruyter, 9783110494969
In:
DGBA Backlist Complete English Language 2000-2014 PART1, De Gruyter, 9783110238570
In:
DGBA Backlist Mathematics 2000-2014 (EN), De Gruyter, 9783110238471
In:
DGBA Mathematics - 2000 - 2014, De Gruyter, 9783110637205
In:
E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2009, De Gruyter, 9783110219517
In:
E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2009, De Gruyter, 9783110219524
In:
E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2009, De Gruyter, 9783110219463
Additional Edition:
ISBN 9783110197013
Language:
English
DOI:
10.1515/9783110203059
URL:
https://doi.org/10.1515/9783110203059
URL:
https://www.degruyter.com/isbn/9783110203059
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