Endomorphisms of Linear Algebraic Groups
Author: Robert Steinberg
Publisher: American Mathematical Soc.
Published: 1968
Total Pages: 113
ISBN-13: 0821812807
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Linear Algebraic Groups and Finite Groups of Lie Type
Author: Gunter Malle
Publisher: Cambridge University Press
Published: 2011-09-08
Total Pages: 324
ISBN-13: 113949953X
DOWNLOAD EBOOKOriginating 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.
Algebraic Groups
Author: J. S. Milne
Publisher: Cambridge University Press
Published: 2017-09-21
Total Pages: 665
ISBN-13: 1107167485
DOWNLOAD EBOOKComprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Algebraic Geometry IV
Author: A.N. Parshin
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 291
ISBN-13: 366203073X
DOWNLOAD EBOOKTwo contributions on closely related subjects: the theory of linear algebraic groups and invariant theory, by well-known experts in the fields. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.
Linear Algebraic Groups
Author: T.A. Springer
Publisher: Springer Science & Business Media
Published: 2010-10-12
Total Pages: 347
ISBN-13: 0817648402
DOWNLOAD EBOOKThe 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.
Representations of Algebraic Groups
Author: Jens Carsten Jantzen
Publisher: American Mathematical Soc.
Published: 2003
Total Pages: 594
ISBN-13: 082184377X
DOWNLOAD EBOOKGives 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.
Robert Steinberg Collected Papers
Author: Robert Steinberg
Publisher: American Mathematical Soc.
Published: 1997
Total Pages: 628
ISBN-13: 9780821805763
DOWNLOAD EBOOKThis volume is a collection of published papers by Robert Steinberg. It contains all of his published papers on group theory, including those on "special" representations (now called Steinberg representations), Coxeter groups, regular nilpotent elements and Galois cohomology. After each paper, there is a section, "Comments on the papers", that contains minor corrections and clarifications and explains how ideas and results have evolved and been used since they first appeared.
Linear Algebraic Groups and Their Representations
Author: Richard S. Elman
Publisher: American Mathematical Soc.
Published: 1993
Total Pages: 215
ISBN-13: 0821851616
DOWNLOAD EBOOK* 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.
Linear Algebraic Groups
Author: James E. Humphreys
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 259
ISBN-13: 1468494430
DOWNLOAD EBOOKJames 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.
Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups
Author: Ross Lawther
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 201
ISBN-13: 0821847694
DOWNLOAD EBOOKLet G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate the Lie algebra of Z(CG(u)), in particular determining its dimension; they prove a succession of theorems of increasing generality, the last of which provides a formula for dim Z(CG(u)) in terms of the labelled diagram associated to the conjugacy class containing u.
