Classifying the Absolute Toral Rank Two Case (De Gruyter Expositions in Mathematics, 42) - Hardcover
Buch 16 von 100: De Gruyter Expositions in Mathematics
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 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.
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Über die Autorin bzw. den Autor
Helmut Strade, Universitty ofHamburg, Germany.
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Simple Lie Algebras over Fields of Positive Characteristic: II. Classifying the Absolute Toral Rank Two Case (De Gruyter Expositions in Mathematics)
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Walter de Gruyter, 2009
ISBN 10: 3110197014
ISBN 13: 9783110197013
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Hardcover. Zustand: Very Good. 1st Edition. Hardcover, vi + 384 pages, NOT ex-library. Clean and bright throughout, with unmarked text, free of inscriptions and stamps, firmly bound. Boards show gentle shelfwear. Published without a dust jacket. -- 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 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 simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type. -- This is the second 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. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, a complete proof for the classification of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristic > 3 is given. -- Contents: Tori in Hamiltonian and Melikian algebras; 1-sections; Sandwich elements and rigid tori; Towards graded algebras; The toral rank 2 case; Supplements to Volume 1; Notations; Bibliography; Index. Bestandsnummer des Verkäufers 005140
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Simple Lie Algebras over Fields of Positive Characteristic, II
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Zustand: Neu. II. Classifying the Absolute Toral Rank Two Case. This volume presents the state of the art of the structure and classification of Lie algebras over fields of positive characteristic. The contents is leading to the forefront of current research in this field. VI,384 Seiten, gebunden (de Gruyter Expositions in Mathematics; Vol. 42/Walter de Gruyter 2009). Früher EUR 179,95. Gewicht: 770 g - Gebunden/Gebundene Ausgabe. Bestandsnummer des Verkäufers 16852
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