Simple Lie Algebras Over Fields Of Positive Characteristic Structure Theory PDF Download
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Author | : Helmut Strade |
Publisher | : Walter de Gruyter |
Total Pages | : 548 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 3110142112 |
Download Simple Lie Algebras Over Fields of Positive Characteristic: Structure theory Book in PDF, ePub and Kindle
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 primesmake this volume an invaluable source and reference for all research mathematicians and advanced graduate students in albegra.
Author | : Helmut Strade |
Publisher | : |
Total Pages | : |
Release | : 2017 |
Genre | : |
ISBN | : |
Download Simple Lie Algebras Over Fields of Positive Characteristic Book in PDF, ePub and Kindle
Author | : Helmut Strade |
Publisher | : Walter de Gruyter |
Total Pages | : 392 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 3110197014 |
Download Simple Lie Algebras Over Fields of Positive Characteristic: Classifying the absolute toral rank two case Book in PDF, ePub and Kindle
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.
Author | : Helmut Strade |
Publisher | : |
Total Pages | : 0 |
Release | : 2009 |
Genre | : |
ISBN | : 9783110197013 |
Download Simple Lie Algebras Over Fields of Positive Characteristics. II. Classifying the Absolute Toral Rank Two Case Book in PDF, ePub and Kindle
Author | : Helmut Strade |
Publisher | : De Gruyter |
Total Pages | : 239 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 9783110262988 |
Download Simple Lie Algebras Over Fields of Positive Characteristic: Completion of the classification Book in PDF, ePub and Kindle
This is the last of three volumes about 'Simple Lie Algebras over Fields of Positive Characteristic' by Helmut Strade, presenting the state of the art of the structure and classification of Lie algebras over fields of positive characteristic. 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.
Author | : H. Strade |
Publisher | : CRC Press |
Total Pages | : 318 |
Release | : 2020-08-11 |
Genre | : Mathematics |
ISBN | : 1000103390 |
Download Modular Lie Algebras and their Representations Book in PDF, ePub and Kindle
This book presents an introduction to the structure and representation theory of modular Lie algebras over fields of positive characteristic. It introduces the beginner to the theory of modular Lie algebras and is meant to be a reference text for researchers.
Author | : Helmut Strade |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 550 |
Release | : 2017-04-24 |
Genre | : Mathematics |
ISBN | : 311051544X |
Download Structure Theory Book in PDF, ePub and Kindle
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. 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. This first volume is devoted to preparing the ground for the classification work to be performed in the second and third volumes. 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 will make this volume an invaluable source and reference for all research mathematicians and advanced graduate students in algebra. The second edition is corrected. Contents Toral subalgebras in p-envelopes Lie algebras of special derivations Derivation simple algebras and modules Simple Lie algebras Recognition theorems The isomorphism problem Structure of simple Lie algebras Pairings of induced modules Toral rank 1 Lie algebras
Author | : Helmut Strade |
Publisher | : |
Total Pages | : 238 |
Release | : 2013 |
Genre | : |
ISBN | : |
Download Simple Lie Algebras Over Fields of Positive Characteristic Book in PDF, ePub and Kindle
Author | : Geoge B. Seligman |
Publisher | : Springer Science & Business Media |
Total Pages | : 175 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642949851 |
Download Modular Lie Algebras Book in PDF, ePub and Kindle
The study of the structure of Lie algebras over arbitrary fields is now a little more than thirty years old. The first papers, to my know ledge, which undertook this study as an end in itself were those of JACOBSON (" Rational methods in the theory of Lie algebras ") in the Annals, and of LANDHERR ("Uber einfache Liesche Ringe") in the Hamburg Abhandlungen, both in 1935. Over fields of characteristic zero, these thirty years have seen the ideas and results inherited from LIE, KILLING, E. CARTAN and WEYL developed and given new depth, meaning and elegance by many contributors. Much of this work is presented in [47, 64, 128 and 234] of the bibliography. For those who find the rationalization for the study of Lie algebras in their connections with Lie groups, satisfying counterparts to these connections have been found over general non-modular fields, with the substitution of the formal groups of BOCHNER [40] (see also DIEUDONNE [108]), or that of the algebraic linear groups of CHEVALLEY [71], for the usual Lie group. In particular, the relation with algebraic linear groups has stimulated the study of Lie algebras of linear transformations. When one admits to consideration Lie algebras over a base field of positive characteristic (such are the algebras to which the title of this monograph refers), he encounters a new and initially confusing scene.
Author | : Helmut Strade |
Publisher | : Walter de Gruyter |
Total Pages | : 548 |
Release | : 2008-08-22 |
Genre | : Mathematics |
ISBN | : 3110197944 |
Download Structure Theory Book in PDF, ePub and Kindle
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 primesmake this volume an invaluable source and reference for all research mathematicians and advanced graduate students in albegra.