Algebraic Q Groups As Abstract Groups PDF Download
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Author | : Olivier Frécon |
Publisher | : American Mathematical Soc. |
Total Pages | : 99 |
Release | : 2018-10-03 |
Genre | : |
ISBN | : 1470429233 |
Download Algebraic Q-Groups as Abstract Groups Book in PDF, ePub and Kindle
The author analyzes the abstract structure of algebraic groups over an algebraically closed field . For of characteristic zero and a given connected affine algebraic Q -group, the main theorem describes all the affine algebraic Q -groups such that the groups and are isomorphic as abstract groups. In the same time, it is shown that for any two connected algebraic Q -groups and , the elementary equivalence of the pure groups and implies that they are abstractly isomorphic. In the final section, the author applies his results to characterize the connected algebraic groups, all of whose abstract automorphisms are standard, when is either Q or of positive characteristic. In characteristic zero, a fairly general criterion is exhibited.
Author | : Jens Carsten Jantzen |
Publisher | : American Mathematical Soc. |
Total Pages | : 594 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 082184377X |
Download Representations of Algebraic Groups Book in PDF, ePub and Kindle
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.
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 | : Clive Reis |
Publisher | : World Scientific Publishing Company |
Total Pages | : 574 |
Release | : 2016-08-30 |
Genre | : Mathematics |
ISBN | : 9814730564 |
Download Abstract Algebra: Introduction To Groups, Rings And Fields With Applications (Second Edition) Book in PDF, ePub and Kindle
This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.
Author | : Gus Lehrer |
Publisher | : Cambridge University Press |
Total Pages | : 396 |
Release | : 1997-01-23 |
Genre | : Mathematics |
ISBN | : 9780521585323 |
Download Algebraic Groups and Lie Groups Book in PDF, ePub and Kindle
This volume contains original research articles by many of the world's leading researchers in algebraic and Lie groups. Its inclination is algebraic and geometic, although analytical aspects are included. The central theme reflects the interests of R. W. Richardson, viz connections between representation theory and the structure and geometry of algebraic groups. All workers on algebraic and Lie groups will find that this book contains a wealth of interesting material.
Author | : Hans Wussing |
Publisher | : Courier Corporation |
Total Pages | : 338 |
Release | : 2007-01-01 |
Genre | : Mathematics |
ISBN | : 0486458687 |
Download The Genesis of the Abstract Group Concept Book in PDF, ePub and Kindle
"It is a pleasure to turn to Wussing's book, a sound presentation of history," declared the Bulletin of the American Mathematical Society. The author, Director of the Institute for the History of Medicine and Science at Leipzig University, traces the axiomatic formulation of the abstract notion of group. 1984 edition.
Author | : Vladimir Platonov |
Publisher | : Academic Press |
Total Pages | : 629 |
Release | : 1993-12-07 |
Genre | : Mathematics |
ISBN | : 0080874592 |
Download Algebraic Groups and Number Theory Book in PDF, ePub and Kindle
This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.
Author | : Vladimir Platonov |
Publisher | : Cambridge University Press |
Total Pages | : 379 |
Release | : 2023-08-31 |
Genre | : Mathematics |
ISBN | : 052111361X |
Download Algebraic Groups and Number Theory Book in PDF, ePub and Kindle
The first volume of a two-volume book offering a comprehensive account of the arithmetic theory of algebraic groups.
Author | : Charles C Pinter |
Publisher | : Courier Corporation |
Total Pages | : 402 |
Release | : 2010-01-14 |
Genre | : Mathematics |
ISBN | : 0486474178 |
Download A Book of Abstract Algebra Book in PDF, ePub and Kindle
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Author | : Bertram A. F. Wehrfritz |
Publisher | : World Scientific |
Total Pages | : 138 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 9789810238742 |
Download Finite Groups Book in PDF, ePub and Kindle
The theory of groups, especially of finite groups, is one of the most delightful areas of mathematics. Its proofs often have elegance and crystalline beauty. This textbook is intended for the reader who has been exposed to about three years of serious mathematics. The notion of a group appears widely in mathematics and even further afield in physics and chemistry, and the fundamental idea should be known to all mathematicians. In this textbook a purely algebraic approach is taken and the choice of material is based upon the notion of conjugacy. The aim is not only to cover basic material, but also to present group theory as a living, vibrant and growing discipline, by including references and discussion of some work up to the present day.