Linear Algebraic Groups
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Linear Algebraic Groups
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Author : James E. Humphreys
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Algebraic Groups written by James E. Humphreys and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
James E. Humphreys is presently Professor of Mathematics at the University of Massachusetts at Amherst. Before this, he held the posts of Assistant Professor of Mathematics at the University of Oregon and Associate Professor of Mathematics at New York University. His main research interests include group theory and Lie algebras. He graduated from Oberlin College in 1961. He did graduate work in philosophy and mathematics at Cornell University and later received hi Ph.D. from Yale University if 1966. In 1972, Springer-Verlag published his first book, "Introduction to Lie Algebras and Representation Theory" (graduate Texts in Mathematics Vol. 9).
Linear Algebraic Groups
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Author : Armand Borel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Linear Algebraic Groups written by Armand Borel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is a revised and enlarged edition of "Linear Algebraic Groups", published by W.A. Benjamin in 1969. The text of the first edition has been corrected and revised. Accordingly, this book presents foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. After establishing these basic topics, the text then turns to solvable groups, general properties of linear algebraic groups and Chevally's structure theory of reductive groups over algebraically closed groundfields. The remainder of the book is devoted to rationality questions over non-algebraically closed fields. This second edition has been expanded to include material on central isogenies and the structure of the group of rational points of an isotropic reductive group. The main prerequisite is some familiarity with algebraic geometry. The main notions and results needed are summarized in a chapter with references and brief proofs.
Linear Algebraic Groups
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Author : T.A. Springer
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-12
Linear Algebraic Groups written by T.A. Springer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-12 with Mathematics categories.
The first edition of this book presented the theory of linear algebraic groups over an algebraically closed field. The second edition, thoroughly revised and expanded, extends the theory over arbitrary fields, which are not necessarily algebraically closed. It thus represents a higher aim. As in the first edition, the book includes a self-contained treatment of the prerequisites from algebraic geometry and commutative algebra, as well as basic results on reductive groups. As a result, the first part of the book can well serve as a text for an introductory graduate course on linear algebraic groups.
Linear Algebraic Groups And Finite Groups Of Lie Type
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Author : Gunter Malle
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-08
Linear Algebraic Groups And Finite Groups Of Lie Type written by Gunter Malle and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-08 with Mathematics categories.
Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.
Linear Algebraic Groups
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Author : Tonny Albert Springer
language : en
Publisher: Springer Science & Business Media
Release Date : 1998
Linear Algebraic Groups written by Tonny Albert Springer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
"[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style⦠[The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literatureâ¦appear for the first time in a text." âMathematical Reviews(Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of the first ten chapters covers the contents of the old book, but the arrangement is somewhat different and there are additions, such as the basic facts about algebraic varieties and algebraic groups over a ground field, as well as an elementary treatment of Tannaka's theorem. These chapters can serve as a text for an introductory course on linear algebraic groups. The last seven chapters are new. They deal with algebraic groups over arbitrary fields. Some of the material has not been dealt with before in other texts, such as Rosenlicht's results about solvable groups in Chapter 14, the theorem of Borel and Tits on the conjugacy over the ground field of maximal split tori in an arbitrary linear algebraic group in Chapter 15, and the Tits classification of simple groups over a ground field in Chapter 17. The book includes many exercises and a subject index." âZentralblatt Math(Review of the Second Edition)
Linear Algebraic Groups And Their Representations
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Author : Richard S. Elman
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Linear Algebraic Groups And Their Representations written by Richard S. Elman 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 1993 with Mathematics categories.
* Brings together a wide variety of themes under a single unifying perspective The proceedings of a conference on Linear algebraic Groups and their Representations - the text gets to grips with the fundamental nature of this subject and its interaction with a wide variety of active areas in mathematics and physics.
Algebraic Groups
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Author : J. S. Milne
language : en
Publisher: Cambridge University Press
Release Date : 2017-09-21
Algebraic Groups written by J. S. Milne and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-21 with Mathematics categories.
Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
An Introduction To Algebraic Geometry And Algebraic Groups
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Author : Meinolf Geck
language : en
Publisher: Oxford University Press
Release Date : 2013-03-14
An Introduction To Algebraic Geometry And Algebraic Groups written by Meinolf Geck and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.
Representations Of Algebraic Groups
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Author : Jens Carsten Jantzen
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Representations Of Algebraic Groups written by Jens Carsten Jantzen 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 2003 with Mathematics categories.
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.
Algebraic Geometry Iv
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Author : A.N. Parshin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Geometry Iv written by A.N. Parshin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The problems being solved by invariant theory are far-reaching generalizations and extensions of problems on the "reduction to canonical form" of various is almost the same thing, projective geometry. objects of linear algebra or, what Invariant theory has a ISO-year history, which has seen alternating periods of growth and stagnation, and changes in the formulation of problems, methods of solution, and fields of application. In the last two decades invariant theory has experienced a period of growth, stimulated by a previous development of the theory of algebraic groups and commutative algebra. It is now viewed as a branch of the theory of algebraic transformation groups (and under a broader interpretation can be identified with this theory). We will freely use the theory of algebraic groups, an exposition of which can be found, for example, in the first article of the present volume. We will also assume the reader is familiar with the basic concepts and simplest theorems of commutative algebra and algebraic geometry; when deeper results are needed, we will cite them in the text or provide suitable references.