Completion of the Classification
Language: English
Published by De Gruyter, 2012
Series: Book 59 of 100 - De Gruyter Expositions in Mathematics
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Seller Inventory # 9783110262988
- Title
- Completion of the Classification
- Author
- Helmut Strade
- Publisher
- De Gruyter
- Publication year
- 2012
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 3110262983
- ISBN 13
- 9783110262988
- Item weight
- 664 grams
- Dimensions
- 246x175x24 mm
- Series
- Book 59 of 100: De Gruyter Expositions in Mathematics
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 last of three volumes. In this monograph the proof of the Classification Theorem presented in the first volume is concluded. It collects all the important results on the topic which can be found only in scattered scientific literature so far.
"Synopsis" may belong to another edition of this title.
About the Author
Helmut Strade, University of Hamburg, Germany.
"About the title" may belong to another edition of this title.
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