Linear Algebraic Groups PDF Download
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Author | : James E. Humphreys |
Publisher | : Springer Science & Business Media |
Total Pages | : 259 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468494430 |
Download Linear Algebraic Groups Book in PDF, ePub and Kindle
James E. Humphreys is a distinguished Professor of Mathematics at the University of Massachusetts at Amherst. He has previously held posts at the University of Oregon and New York University. His main research interests include group theory and Lie algebras, and this graduate level text is an exceptionally well-written introduction to everything about linear algebraic groups.
Author | : T.A. Springer |
Publisher | : Springer Science & Business Media |
Total Pages | : 347 |
Release | : 2010-10-12 |
Genre | : Mathematics |
ISBN | : 0817648402 |
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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.
Author | : Armand Borel |
Publisher | : Springer Science & Business Media |
Total Pages | : 301 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461209412 |
Download Linear Algebraic Groups Book in PDF, ePub and Kindle
This revised, enlarged edition of Linear Algebraic Groups (1969) starts by presenting foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. It then turns to solvable groups, general properties of linear algebraic groups, and Chevally’s structure theory of reductive groups over algebraically closed groundfields. It closes with a focus on rationality questions over non-algebraically closed fields.
Author | : Gunter Malle |
Publisher | : Cambridge University Press |
Total Pages | : 324 |
Release | : 2011-09-08 |
Genre | : Mathematics |
ISBN | : 113949953X |
Download Linear Algebraic Groups and Finite Groups of Lie Type Book in PDF, ePub and Kindle
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.
Author | : Richard S. Elman |
Publisher | : American Mathematical Soc. |
Total Pages | : 215 |
Release | : 1993 |
Genre | : Mathematics |
ISBN | : 0821851616 |
Download Linear Algebraic Groups and Their Representations Book in PDF, ePub and Kindle
* 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.
Author | : Michel Waldschmidt |
Publisher | : Springer Science & Business Media |
Total Pages | : 649 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662115697 |
Download Diophantine Approximation on Linear Algebraic Groups Book in PDF, ePub and Kindle
The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.
Author | : Willem Adriaan de Graaf |
Publisher | : CRC Press |
Total Pages | : 324 |
Release | : 2017-08-07 |
Genre | : Mathematics |
ISBN | : 1498722911 |
Download Computation with Linear Algebraic Groups Book in PDF, ePub and Kindle
Designed as a self-contained account of a number of key algorithmic problems and their solutions for linear algebraic groups, this book combines in one single text both an introduction to the basic theory of linear algebraic groups and a substantial collection of useful algorithms. Computation with Linear Algebraic Groups offers an invaluable guide to graduate students and researchers working in algebraic groups, computational algebraic geometry, and computational group theory, as well as those looking for a concise introduction to the theory of linear algebraic groups.
Author | : Meinolf Geck |
Publisher | : Oxford University Press |
Total Pages | : 321 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 019967616X |
Download An Introduction to Algebraic Geometry and Algebraic Groups Book in PDF, ePub and Kindle
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.
Author | : J. S. Milne |
Publisher | : Cambridge University Press |
Total Pages | : 665 |
Release | : 2017-09-21 |
Genre | : Mathematics |
ISBN | : 1107167485 |
Download Algebraic Groups Book in PDF, ePub and Kindle
Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Author | : Armand Borel |
Publisher | : American Mathematical Soc. |
Total Pages | : 184 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821802887 |
Download Essays in the History of Lie Groups and Algebraic Groups Book in PDF, ePub and Kindle
Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passagefrom local to global, the author takes Lie's theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former,Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large.The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groupsand algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields.The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development.