UID:
almahu_9949462252302882
Format:
1 online resource (540 p.)
Edition:
Reprint 2014
ISBN:
9783110197945
,
9783110494969
Series Statement:
De Gruyter Expositions in Mathematics , 38
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 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.
Note:
Frontmatter --
,
Contents --
,
Introduction --
,
Chapter 1. Toral subalgebras in p-envelopes --
,
Chapter 2. Lie algebras of special --
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derivations --
,
Chapter 3. Derivation simple algebras and --
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modules --
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Chapter 4. Simple Lie algebras --
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Chapter 5. Recognition theorems --
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Chapter 6. The isomorphism problem --
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Chapter 7. Structure of simple Lie algebras --
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Chapter 8. Pairings of induced modules --
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Chapter 9. Toral rank 1 Lie algebras --
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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 2008, De Gruyter, 9783110212129
In:
E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2008, De Gruyter, 9783110212136
In:
E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008, De Gruyter, 9783110209082
Additional Edition:
ISBN 9783110142112
Language:
English
DOI:
10.1515/9783110197945
URL:
https://doi.org/10.1515/9783110197945
URL:
https://www.degruyter.com/isbn/9783110197945
