Introduction To Affine Algebraic Groups

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Introduction To Affine Group Schemes

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Author : W.C. Waterhouse
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Affine Group Schemes written by W.C. Waterhouse and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Ah Love! Could you and I with Him consl?ire To grasp this sorry Scheme of things entIre' KHAYYAM People investigating algebraic groups have studied the same objects in many different guises. My first goal thus has been to take three different viewpoints and demonstrate how they offer complementary intuitive insight into the subject. In Part I we begin with a functorial idea, discussing some familiar processes for constructing groups. These turn out to be equivalent to the ring-theoretic objects called Hopf algebras, with which we can then con struct new examples. Study of their representations shows that they are closely related to groups of matrices, and closed sets in matrix space give us a geometric picture of some of the objects involved. This interplay of methods continues as we turn to specific results. In Part II, a geometric idea (connectedness) and one from classical matrix theory (Jordan decomposition) blend with the study of separable algebras. In Part III, a notion of differential prompted by the theory of Lie groups is used to prove the absence of nilpotents in certain Hopf algebras. The ring-theoretic work on faithful flatness in Part IV turns out to give the true explanation for the behavior of quotient group functors. Finally, the material is connected with other parts of algebra in Part V, which shows how twisted forms of any algebraic structure are governed by its automorphism group scheme.

Introduction To Affine Algebraic Groups

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Author : Gerhard Paul Hochschild
language : en
Publisher:
Release Date : 1971

Introduction To Affine Algebraic Groups written by Gerhard Paul Hochschild and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.

Introduction To Affine Group Schemes

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Author : William C. Waterhouse
language : en
Publisher:
Release Date : 1979-01-01

Introduction To Affine Group Schemes written by William C. Waterhouse and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-01-01 with Group schemes (Mathematics) categories.

An Introduction To Algebraic Geometry And Algebraic Groups

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Author : Meinolf Geck
language : en
Publisher: Oxford University Press
Release Date : 2013-03-14

An Introduction To Algebraic Geometry And Algebraic Groups written by Meinolf Geck and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

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.

Linear Algebraic Groups

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Author : T.A. Springer
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-12

Linear Algebraic Groups written by T.A. Springer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-12 with Mathematics categories.

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.

Affine Sets And Affine Groups

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Author : D. G. Northcott
language : en
Publisher: Cambridge University Press
Release Date : 1980-05-08

Affine Sets And Affine Groups written by D. G. Northcott and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-05-08 with Mathematics categories.

In these notes, first published in 1980, Professor Northcott provides a self-contained introduction to the theory of affine algebraic groups for mathematicians with a basic knowledge of communicative algebra and field theory. The book divides into two parts. The first four chapters contain all the geometry needed for the second half of the book which deals with affine groups. Alternatively the first part provides a sure introduction to the foundations of algebraic geometry. Any affine group has an associated Lie algebra. In the last two chapters, the author studies these algebras and shows how, in certain important cases, their properties can be transferred back to the groups from which they arose. These notes provide a clear and carefully written introduction to algebraic geometry and algebraic groups.

Representations Of Algebraic Groups

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Author : Jens Carsten Jantzen
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Representations Of Algebraic Groups written by Jens Carsten Jantzen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Linear algebraic groups categories.

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.

Actions And Invariants Of Algebraic Groups

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Author : Walter Ricardo Ferrer Santos
language : en
Publisher: CRC Press
Release Date : 2017-09-19

Actions And Invariants Of Algebraic Groups written by Walter Ricardo Ferrer Santos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-19 with Mathematics categories.

Actions and Invariants of Algebraic Groups, Second Edition presents a self-contained introduction to geometric invariant theory starting from the basic theory of affine algebraic groups and proceeding towards more sophisticated dimensions." Building on the first edition, this book provides an introduction to the theory by equipping the reader with the tools needed to read advanced research in the field. Beginning with commutative algebra, algebraic geometry and the theory of Lie algebras, the book develops the necessary background of affine algebraic groups over an algebraically closed field, and then moves toward the algebraic and geometric aspects of modern invariant theory and quotients.

Introduction To Algebraic Geometry And Algebraic Groups

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Author :
language : en
Publisher: Elsevier
Release Date : 1980-01-01

Introduction To Algebraic Geometry And Algebraic Groups written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-01 with Mathematics categories.

Introduction to Algebraic Geometry and Algebraic Groups

Introduction To The Theory Of Formal Groups

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Author : Jean A. Dieudonne
language : en
Publisher: CRC Press
Release Date : 2020-01-29

Introduction To The Theory Of Formal Groups written by Jean A. Dieudonne and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-29 with Mathematics categories.

The concept of formal Lie group was derived in a natural way from classical Lie theory by S. Bochner in 1946, for fields of characteristic 0. Its study over fields of characteristic p > 0 began in the early 1950’s, when it was realized, through the work of Chevalley, that the familiar “dictionary” between Lie groups and Lie algebras completely broke down for Lie algebras of algebraic groups over such a field. This volume, starts with the concept of C-group for any category C (with products and final object), but the author’s do not exploit it in its full generality. The book is meant to be introductory to the theory, and therefore the necessary background to its minimum possible level is minimised: no algebraic geometry and very little commutative algebra is required in chapters I to III, and the algebraic geometry used in chapter IV is limited to the Serre- Chevalley type (varieties over an algebraically closed field).