Groups Generators Syzygies And Orbits In Invariant Theory

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Groups Generators Syzygies And Orbits In Invariant Theory

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Author : V. L. Popov
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-01-05

Groups Generators Syzygies And Orbits In Invariant Theory written by V. L. Popov 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 2011-01-05 with Mathematics categories.

The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups. Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invariant theory. Its point of view is unique in that it combines both modern and classical approaches to the subject. The introductory chapter sets the historical stage for the subject, helping to make the book accessible to nonspecialists.

Groups Generators Syzygies And Orbits In Invariant Theory

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Author : Vladimir Leonidovich Popov
language : en
Publisher:
Release Date : 1992

Groups Generators Syzygies And Orbits In Invariant Theory written by Vladimir Leonidovich Popov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Invariants categories.

The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups. Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invar.

Geometric Invariant Theory

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Author : David Mumford
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-03-29

Geometric Invariant Theory written by David Mumford 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 1994-03-29 with Mathematics categories.

This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan. It includes a fully updated bibliography of work in this area.

Computational Invariant Theory

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Author : Harm Derksen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Computational Invariant Theory written by Harm Derksen 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 2013-04-17 with Mathematics categories.

Invariant theory is a subject with a long tradition and an astounding abil ity to rejuvenate itself whenever it reappears on the mathematical stage. Throughout the history of invariant theory, two features of it have always been at the center of attention: computation and applications. This book is about the computational aspects of invariant theory. We present algorithms for calculating the invariant ring of a group that is linearly reductive or fi nite, including the modular case. These algorithms form the central pillars around which the book is built. To prepare the ground for the algorithms, we present Grabner basis methods and some general theory of invariants. Moreover, the algorithms and their behavior depend heavily on structural properties of the invariant ring to be computed. Large parts of the book are devoted to studying such properties. Finally, most of the applications of in variant theory depend on the ability to calculate invariant rings. The last chapter of this book provides a sample of applications inside and outside of mathematics.

Algebraic Geometry Iv

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Author : A.N. Parshin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Algebraic Geometry Iv written by A.N. Parshin 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.

The problems being solved by invariant theory are far-reaching generalizations and extensions of problems on the "reduction to canonical form" of various is almost the same thing, projective geometry. objects of linear algebra or, what Invariant theory has a ISO-year history, which has seen alternating periods of growth and stagnation, and changes in the formulation of problems, methods of solution, and fields of application. In the last two decades invariant theory has experienced a period of growth, stimulated by a previous development of the theory of algebraic groups and commutative algebra. It is now viewed as a branch of the theory of algebraic transformation groups (and under a broader interpretation can be identified with this theory). We will freely use the theory of algebraic groups, an exposition of which can be found, for example, in the first article of the present volume. We will also assume the reader is familiar with the basic concepts and simplest theorems of commutative algebra and algebraic geometry; when deeper results are needed, we will cite them in the text or provide suitable references.

Invariant Theory In All Characteristics

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Author : Harold Edward Alexander Eddy Campbell
language : en
Publisher: American Mathematical Soc.
Release Date :

Invariant Theory In All Characteristics written by Harold Edward Alexander Eddy Campbell 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 with Science categories.

This volume includes the proceedings of a workshop on Invariant Theory held at Queen's University (Ontario). The workshop was part of the theme year held under the auspices of the Centre de recherches mathematiques (CRM) in Montreal. The gathering brought together two communities of researchers: those working in characteristic 0 and those working in positive characteristic. The book contains three types of papers: survey articles providing introductions to computational invarianttheory, modular invariant theory of finite groups, and the invariant theory of Lie groups; expository works recounting recent research in these three areas and beyond; and open problems of current interest. The book is suitable for graduate students and researchers working in invarianttheory.

Classical Invariant Theory

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Author : Peter J. Olver
language : en
Publisher: Cambridge University Press
Release Date : 1999-01-13

Classical Invariant Theory written by Peter J. Olver 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 1999-01-13 with Mathematics categories.

The book is a self-contained introduction to the results and methods in classical invariant theory.

Representations And Invariants Of The Classical Groups

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Author : Roe Goodman
language : en
Publisher: Cambridge University Press
Release Date : 2000-01-13

Representations And Invariants Of The Classical Groups written by Roe Goodman 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 2000-01-13 with Mathematics categories.

More than half a century has passed since Weyl's 'The Classical Groups' gave a unified picture of invariant theory. This book presents an updated version of this theory together with many of the important recent developments. As a text for those new to the area, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.

Actions And Invariants Of Algebraic Groups

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Author : Walter Ferrer Santos
language : en
Publisher: CRC Press
Release Date : 2005-04-26

Actions And Invariants Of Algebraic Groups written by Walter 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 2005-04-26 with Mathematics categories.

Actions and Invariants of Algebraic Groups presents a self-contained introduction to geometric invariant theory that links the basic theory of affine algebraic groups to Mumford's more sophisticated theory. The authors systematically exploit the viewpoint of Hopf algebra theory and the theory of comodules to simplify and compactify many of the rele

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.