Inhaltsangabe
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.
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Über die Autorin bzw. den Autor
Helmut Strade, University of Hamburg, Germany.
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This is the third part of a three-volume book about the classification of the simple Lie algebras over algebraically closed fields of characteristic > 3. The first volume contains the methods, examples and a first classification result, while in the second volume the proof for the case of absolute toral rank 2 simple Lie algebras is completed. Based on these results the present third volume completes the Classification proof for the general case.
One of the very important intermediate results is the decision when elements act nilpotently on the whole algebra. This result then allows to describe 2-sections with respect to a torus of maximal dimension in a minimal p-envelope. Different methods apply for the cases that
- such a torus exists which is non-standard (giving the Melikian algebras),
- such a torus exists which has only solvable roots (giving some Special algebras and some Block algebras),
- no torus of maximal dimension of these two types exists (giving the classical and most of the Cartan type algebras).
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Simple Lie Algebras over Fields of Positive Characteristic 3
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Gebunden. Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. The book under review will surely become a primary source of reference on simple Lie algebras of positive characteristic. Its publication makes the achievements in this field accessible to a large group of mathematicians. Mathematical Reviews . Bestandsnummer des Verkäufers 4456290
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Buch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 252 pp. Englisch. Bestandsnummer des Verkäufers 9783110262988
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Buch. Zustand: Neu. Completion of the Classification | Helmut Strade | Buch | X | Englisch | 2012 | De Gruyter | EAN 9783110262988 | Verantwortliche Person für die EU: Walter de Gruyter GmbH, De Gruyter GmbH, Genthiner Str. 13, 10785 Berlin, productsafety[at]degruyterbrill[dot]com | Anbieter: preigu Print on Demand. Bestandsnummer des Verkäufers 106532045
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Buch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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 > 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: > 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.Walter de Gruyter, Genthiner Straße 13, 10785 Berlin 252 pp. Englisch. Bestandsnummer des Verkäufers 9783110262988
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Hardback. Zustand: New. 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. Bestandsnummer des Verkäufers LU-9783110262988
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Hardback. Zustand: New. 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. Bestandsnummer des Verkäufers LU-9783110262988
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