Cover of: Linear algebraic groups | James E. Humphreys

Linear algebraic groups

  • 253 Pages
  • 2.88 MB
  • 5217 Downloads
  • English
by
Springer-Verlag , New York
Linear algebraic gr
StatementJames E. Humphreys.
SeriesGraduate texts in mathematics -- 21.
The Physical Object
Paginationxvi, 253 p. ;
ID Numbers
Open LibraryOL18434252M
ISBN 100387901086

Thus far, we have covered the first ten chapters of this book, and have reached the following (unfortunately) unfavorable conclusion of this text.

This text is relatively self-contained with fairly standard treatment of the subject of linear algebraic groups as varieties over an algebraic closed field (not necessarily characteristic 0).Cited by: 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 by:   Linear Algebraic Groups entirely avoids the use of scheme theory.

Humphreys mentions in the preface that part of the motivation to write the textbook in the first place was the lack of an elementary treatment of the subject/5.

Description Linear algebraic groups PDF

"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.

This book is a revised and enlarged edition of "Linear Algebraic Groups", published by W.A. Benjamin in The text of the first edition has been Linear algebraic groups book and revised.

Accordingly, this book presents foundational material on algebraic groups, Lie algebras, transformation spaces, and quotientBrand: Springer-Verlag New York. This revised, enlarged edition of Linear Algebraic Groups () starts by presenting foundational material on algebraic groups, Lie algebras, transformation spaces, and Linear algebraic groups book spaces.

It then turns to solvable groups, general properties of linear algebraic groups, and Chevally's structure theory of reductive groups over algebraically closed 4/5(1). In mathematics, a linear algebraic group is a subgroup of the group of invertible n×n matrices (under matrix multiplication) that is defined by polynomial equations.

An example is the orthogonal group, defined by the relation M T M = 1 where M T is the transpose of M. Many Lie groups can be viewed as linear algebraic groups over the field of real or complex numbers. This book is a revised and enlarged edition of "Linear Algebraic Groups", published by W.A.

Benjamin in 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.

Every time I’ve taught the course (undergraduate), I’ve been saddled with someone else’s choice of text. And they’ve generally been isomorphic (the same) and not particularly inspiring.

So I’m going with speculation here - in terms of what I think. This revised, enlarged edition of Linear Algebraic Groups () starts by presenting foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces.

Details Linear algebraic groups EPUB

It then turns to solvable groups, general properties of linear algebraic groups, and Chevally’s structure theory of reductive groups over algebraically closed groundfields.

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.5/5(1).

The first book I read on algebraic groups was An Introduction to Algebraic Geometry and Algebraic Groups by Meinolf Geck. As I recall, the book includes a lot of examples about the classical matrix groups, and gives elementary accounts of such things like computing the tangent space at the identity to get the Lie algebra.

"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.5/5(1). The first edition of this book presented the theory of linear algebraic groups over an algebraically closed field.

This second edition, thoroughly revised and expanded, extends the theory over arbitrary fields, which are not necessarily algebraically closed. Linear Algebraic Groups "Exceptionally well-written and ideally suited either for independent reading or as a graduate level text for an introduction to everything about linear algebraic groups."—MATHEMATICAL REVIEWS.

From the PublisherPrice: $ 1. Some Algebraic Geometry Linear Algebraic Groups, First Properties Commutative Algebraic Groups Derivations, Differentials, Lie Algebras Topological Properties of Morphisms, Applications Parabolic Subgroups, Borel Subgroups, Solvable Groups Weyl Group, Roots, Root Datum Reductive Groups 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. Book Description. 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.

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 2/5(1).

Linear Algebraic Groups Fiona Murnaghan Abstract. We give a summary, without proofs, of basic properties of linear algebraic groups, with particular emphasis on reductive algebraic groups. Algebraic groups Let K be an algebraically closed field.

An algebraic K-group G is an algebraic. Computation with Linear Algebraic Groups - CRC Press Book 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.

$\begingroup$ There is this book by Malle and Testerman, Linear Algebraic Groups and Finite groups of Lie type, what do you think of it. $\endgroup$ – user Sep 8 '12 at $\begingroup$ @BenjaLim I have just read the preface and the beginning of the first chapter, and maybe it is not the best place to learn about algebraic groups, if.

Algebraic Groups The theory of group schemes of finite type over a field. J.S.

Download Linear algebraic groups EPUB

Milne Version Decem This is a rough preliminary version of the book published by CUP inThe final version is substantially rewritten, and the numbering has changed. Linear Algebraic Groups by James E. Humphreys,available at Book Depository with free delivery worldwide/5(9).

Linear Algebraic Groups James E. Humphreys (auth.) James E. Humphreys is presently Professor of Mathematics at the University of Massachusetts at Amherst.

Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them., Free ebooks since [email protected] A connected (irreducible) linear algebraic group has a maximal solvable connected normal subgroup such that the quotient group is a central product of simple algebraic groups, a socalled semisimple algebraic group.

Thus, one is led to the study of semisimple groups and connected solvable groups. 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.

Is there a book on linear algebraic groups using the scheme language (i.e. not Springer or Borel, but like Waterhouse, but more in-depth). The book should discuss topics like Borel subgroups etc. (Related question: Books on reductive groups using scheme theory). $\begingroup$ I don't remember all these details when I learned linear algebraic groups.

But I do remember constantly switching between Borel, Springer, and Humphreys when I was stuck on one book's explanation of something. $\endgroup$ – D_S Dec 31 '17 at Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more.

Algebraic groups play much the same role for algebraists as Lie groups play for analysts. This book is the first comprehensive introduction to the theory of algebraic group schemes over fields that includes the structure theory of semisimple algebraic groups, and is written in Cited by: LECTURES ON LINEAR ALGEBRAIC GROUPS.

Currently this section contains no detailed description for the page, will update this page soon. Author(s): NA. NA Pages. Download / View book. Similar Books. Notes on Group Theory. This note covers the following topics: Notation for sets and functions, Basic group theory, The Symmetric Group, Group actions.Linear algebraic groups.

New York: Springer-Verlag. MLA Citation. Humphreys, James E. Linear algebraic groups / James E. Humphreys Springer-Verlag New York Australian/Harvard Citation.

Humphreys, James E.Linear algebraic groups / James E. Humphreys Springer-Verlag New York. Wikipedia Citation.