5 edition of **Algebraic Groups** found in the catalog.

Algebraic Groups

Wim H. Hesselink

- 313 Want to read
- 0 Currently reading

Published
**November 1987**
by Springer
.

Written in English

**Edition Notes**

Contributions | Arjeh M. Cohen (Editor), T. A. Springer (Editor), Jan R. Strooker (Editor) |

The Physical Object | |
---|---|

Number of Pages | 284 |

ID Numbers | |

Open Library | OL7443946M |

ISBN 10 | 0387182349 |

ISBN 10 | 9780387182346 |

Abstract Algebra: A First Course. By Dan Saracino I haven't seen any other book explaining the basic concepts of abstract algebra this beautifully. It is divided in two parts and the first part is only about groups though. The second part is an in. An algebraic subgroup of an algebraic group is a Zariski-closed subgroup. Generally these are taken to be connected (or irreducible as a variety) as well. Another way of expressing the condition is as a subgroup that is also a subvariety. This may also be generalized by allowing schemes in place of varieties.

Full text access 9. Normal subgroup structure of groups of rational points of algebraic groups Pages Download PDF. ( views) Algebraic Groups, Lie Groups, and their Arithmetic Subgroups by J. S. Milne, This work is a modern exposition of the theory of algebraic group schemes, Lie groups, and their arithmetic subgroups. Algebraic groups are groups defined by polynomials. Those in this book can all be realized as groups of matrices.

The chapter provides basic general definitions concerning algebraic groups and their representations. In addition, it also proves the Borel-Weil-Bott theorem and Serre duality. From these two results it is easily deduced the complete reducibility of all finite dimensional modules for algebraic groups in characteristic zero. 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 .

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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: 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).

Despite being rooted in algebraic geometry, the subject has a fair mix of non-algebraic geometric Cited by: 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 the language of modern algebraic geometry.

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. Back in print from the AMS, the first part of this book is an introduction to the general theory of representations of algebraic group schemes.

Here, Janzten describes important basic notions. 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.

Mathematics books by J.S. Milne Algebraic Groups: the theory of group schemes of finite type over a field J.S. Milne This is a comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, but with minimal prerequisites.

The final manuscript was sent to CUP. This book represents my attempt to write a modern successor to the three standard works, all titled “Linear Algebraic Groups”, by Borel, Humphreys, and Springer.

More speciﬁcally, it is an exposition of the theory of group schemes of ﬁnite type over a ﬁeld, based on modern algebraic geometry, but with minimal prerequisites. Basic Algebra Books. Other algebraic structures (groups, fields) also are introduced. Author(s): David Joyce, Clark University.

Pages. College Algebra for STEM. This book is designed specifically as a College Algebra course for prospective STEM students. Topics covered includes: Review of Beginning/Intermediate Algebra, Functions and.

thereby giving representations of the group on the homology groups of the space. If there is torsion in the homology these representations require something other than ordinary character theory to be understood.

This book is written for students who are studying nite group representation theory beyond the level of a rst course in abstract Size: 1MB. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number Edition: 1.

Algebraic groups have applications to several areas of pure mathematics. For instance, they are notably central to the Langlands program in Number Theory.

They can also be a good way to construct an important class of nite groups, called nite groups of Lie type. These groups arise as xed point sets of certain types.

Book description. 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 the language of modern algebraic by: One of the satisfying things about reading Humphreys' books is the parsimonious approach he uses.

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.

Back in print from the AMS, the first part of this book is an introduction to the general theory of representations of algebraic group schemes. Here, Janzten describes important basic notions: induction functors, cohomology, quotients, Frobenius kernels, and reduction mod \(p\), among others.

Algebraic Groups and Class Fields. It seems that you're in USA. We have a dedicated site for USA Algebraic Curves. Pages Serre, Jean-Pierre Book Title Algebraic Groups and Class Fields Authors. Jean-Pierre Serre; Series Title Graduate Texts in MathematicsBrand: Springer-Verlag New York.

Try the new Google Books. Check out the new look and enjoy easier access to your favorite features. Try it now. No thanks. Try the new Google Books Buy eBook - $ Get this book in print Chapter V Algebraic Groups.

Bibliography for Chapter V. Chapter VI Galois Theory of Differential Fields. Bibliography for Chapter VI. For problems you can solve problems in the above books but there is the best book for problems: Halmos, Linear Algebra Problem Book.

For applications you might want to look at well known books such as Applied Linear Algebra by. Algebraic Groups and Class Fields book. Read reviews from world’s largest community for readers.4/5(2). theory of such groups as the general linear groups GL n(k), the special linear groups SL n(k), the special orthogonal groups SO n(k), and the symplectic groups Sp2 n(k) over an algebraically closed field k.

These groups are algebraic groups, and we shall look only at representations G —> GL(V) that are homomorphisms of algebraic groups. Geometric Group Theory Preliminary Version Under revision. The goal of this book is to present several central topics in geometric group theory, primarily related to the large scale geometry of infinite groups and spaces on which such groups act, and to illustrate them with fundamental theorems such as Gromov’s Theorem on groups of polynomial growth.If you're interested in the theory of linear algebraic groups, Linear Algebraic Groups by Humphreys is a great book.

The other two standard references are the books (with the same name) by Springer and Borel. All of the algebraic geometry you need to know is built from scratch in any of those books.Introduction to Algebraic Geometry and Algebraic Groups (ISSN series) by Michel Demazure.