Simple Lie Algebras over Fields of Positive Characteristic. / Volume I, : Structure Theory / / Helmut Strade.
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...
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Superior document: | Title is part of eBook package: De Gruyter DG Expositions in Mathematics Backlist eBook Package |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2008] ©2004 |
Year of Publication: | 2008 |
Edition: | Reprint 2014 |
Language: | English |
Series: | De Gruyter Expositions in Mathematics ,
38 |
Online Access: | |
Physical Description: | 1 online resource (540 p.) |
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Other title: | Frontmatter -- Contents -- Introduction -- Chapter 1. Toral subalgebras in p-envelopes -- Chapter 2. Lie algebras of special -- derivations -- Chapter 3. Derivation simple algebras and -- modules -- Chapter 4. Simple Lie algebras -- Chapter 5. Recognition theorems -- Chapter 6. The isomorphism problem -- Chapter 7. Structure of simple Lie algebras -- Chapter 8. Pairings of induced modules -- Chapter 9. Toral rank 1 Lie algebras -- Backmatter |
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Summary: | 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. |
Format: | Mode of access: Internet via World Wide Web. |
ISBN: | 9783110197945 9783110494969 9783110238570 9783110238471 9783110637205 9783110212129 9783110212136 9783110209082 |
ISSN: | 0938-6572 ; |
DOI: | 10.1515/9783110197945 |
Access: | restricted access |
Hierarchical level: | Monograph |
Statement of Responsibility: | Helmut Strade. |