Download or read book Simple Lie Algebras Over Fields of Positive Characteristic Structure theory written by Helmut Strade and published by Walter de Gruyter. This book was released on 2004 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Simple Lie algebras over fields of positive characteristic written by Helmut Strade and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Simple Lie Algebras Over Fields of Positive Characteristic Classifying the absolute toral rank two case written by Helmut Strade and published by Walter de Gruyter. This book was released on 2004 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Simple Lie Algebras Over Fields of Positive Characteristics II Classifying the Absolute Toral Rank Two Case written by Helmut Strade and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Simple Lie Algebras Over Fields of Positive Characteristic Completion of the classification written by Helmut Strade and published by De Gruyter. This book was released on 2012 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Simple Lie Algebras Over Fields of Positive Characteristic written by and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Simple Lie Algebras Over Fields of Positive Characteristic written by Helmut Strade and published by . This book was released on 2013 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Classification of the Simple Lie Algebras Over Fields with Positive Characteristic written by Helmut Strade and published by . This book was released on 2000 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Gradings on Simple Lie Algebras written by Alberto Elduque and published by American Mathematical Soc.. This book was released on 2013 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a self-contained exposition of the classification of gradings by arbitrary groups on classical simple Lie algebras over algebraically closed fields of characteristic not equal to 2 as well as on some non-classical simple Lie algebras in positive characteristic. Other important algebras also enter the stage: matrix algebras, the octonions, and the Albert algebra. Most of the presented results are recent and have not yet appeared in book form.
Download or read book Modular Lie Algebras written by Geoge B. Seligman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modular Lie Algebras and their Representations written by H. Strade and published by CRC Press. This book was released on 2020-08-11 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Simple Lie Algebras Over Fields of Positive Characteristic 02 Classifying the Absolute Toral Rank Two Case written by Helmut Strade and published by de Gruyter. This book was released on 2017-04-15 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second volume, the author presents the state of the art of the structure and classification of Lie algebras over fields of positive characteristic, an important topic in algebra. The contents of the book are leading to the forefront of current research in this field.
Download or read book Modular Lie Algebras written by George B. Seligman and published by . This book was released on 1967 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Representations of Algebraic Groups written by Jens Carsten Jantzen and published by American Mathematical Soc.. This book was released on 2003 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Download or read book Lie Theory written by Jean-Philippe Anker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: * First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.
Download or read book Notes on Simple Lie Algebras Over a Field of Characteristic 2 written by Alexander Nikolaevich Grishkov and published by . This book was released on 2005 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Classifying the Absolute Toral Rank Two Case written by Helmut Strade and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-04-10 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
