Simple Lie Algebras Over Fields Of Positive Characteristics Ii Classifying The Absolute Toral Rank Two Case
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Simple Lie Algebras Over Fields Of Positive Characteristic Classifying The Absolute Toral Rank Two Case
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Author : Helmut Strade
language : en
Publisher: Walter de Gruyter
Release Date : 2004
Simple Lie Algebras Over Fields Of Positive Characteristic Classifying The Absolute Toral Rank Two Case written by Helmut Strade and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Classifying The Absolute Toral Rank Two Case
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Author : Helmut Strade
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-04-10
Classifying The Absolute Toral Rank Two Case written by Helmut Strade and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-10 with Mathematics categories.
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
Simple Lie Algebras Over Fields Of Positive Characteristic Structure Theory
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Author : Helmut Strade
language : en
Publisher: Walter de Gruyter
Release Date : 2004
Simple Lie Algebras Over Fields Of Positive Characteristic Structure Theory written by Helmut Strade and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Mathematical Modeling And Supercomputer Technologies
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Author : Dmitry Balandin
language : en
Publisher: Springer Nature
Release Date : 2025-03-02
Mathematical Modeling And Supercomputer Technologies written by Dmitry Balandin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-02 with Computers categories.
This book constitutes the refereed proceedings of the 24th International Conference on Mathematical Modeling and Supercomputer Technologies , MMST 2024, held in Nizhni Novgorod, Russia, during November 18–21 2024. The 17 full papers and 3 short papers included in this book were carefully reviewed and selected from 39 submissions. They were organized in topical sections as follows: artificial intelligence and supercomputer simulation; computing in optimization and optimal control; computational methods for mathematical models analysis.
Gradings On Simple Lie Algebras
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Author : Alberto Elduque
language : en
Publisher: American Mathematical Soc.
Release Date : 2013
Gradings On Simple Lie Algebras written by Alberto Elduque and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
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.
Lie Algebras And Related Topics
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Author : Marina Avitabile
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-11-30
Lie Algebras And Related Topics written by Marina Avitabile and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-30 with Mathematics categories.
This volume contains the proceedings of the Workshop on Lie Algebras, in honor of Helmut Strade's 70th Birthday, held from May 22-24, 2013, at the Università degli Studi di Milano-Bicocca, Milano, Italy. Lie algebras are at the core of several areas of mathematics, such as, Lie groups, algebraic groups, quantum groups, representation theory, homogeneous spaces, integrable systems, and algebraic topology. The first part of this volume combines research papers with survey papers by the invited speakers. The second part consists of several collections of problems on modular Lie algebras, their representations, and the conjugacy of their nilpotent elements as well as the Koszulity of (restricted) Lie algebras and Lie properties of group algebras or restricted universal enveloping algebras.
Simple Lie Algebras Over Fields Of Positive Characteristics Ii Classifying The Absolute Toral Rank Two Case
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Author : Helmut Strade
language : en
Publisher:
Release Date : 2009
Simple Lie Algebras Over Fields Of Positive Characteristics Ii Classifying The Absolute Toral Rank Two Case written by Helmut Strade and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Complementation Of Normal Subgroups
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Author : Joseph Kirtland
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-09-11
Complementation Of Normal Subgroups written by Joseph Kirtland and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-11 with Mathematics categories.
Starting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups. The contents cover a wide range of material from reduction theorems and subgroups in the derived and lower nilpotent series to abelian normal subgroups and formations. Contents Prerequisites The Schur-Zassenhaus theorem: A bit of history and motivation Abelian and minimal normal subgroups Reduction theorems Subgroups in the chief series, derived series, and lower nilpotent series Normal subgroups with abelian sylow subgroups The formation generation Groups with specific classes of subgroups complemented
Completion Of The Classification
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Author : Helmut Strade
language : en
Publisher: Walter de Gruyter
Release Date : 2012-12-19
Completion Of The Classification written by Helmut Strade and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-19 with Mathematics categories.
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.
Developments And Retrospectives In Lie Theory
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Author : Geoffrey Mason
language : en
Publisher: Springer
Release Date : 2014-10-31
Developments And Retrospectives In Lie Theory written by Geoffrey Mason and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-31 with Mathematics categories.
The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. These workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. At the beginning, the top universities in California and Utah hosted the meetings which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. The contributors to this volume have all participated in these Lie theory workshops and include in this volume expository articles which cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned-above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.