Invariant Theory In All Characteristics

Author : Harold Edward Alexander Eddy Campbell,David L. Wehlau
Publisher : American Mathematical Soc.
Page : 305 pages
File Size : 41,7 Mb
Release : 2004
Category : Invariants
ISBN : 9780821832448

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Invariant Theory in All Characteristics by Harold Edward Alexander Eddy Campbell,David L. Wehlau Pdf

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.

Author : Harold Edward Alexander Eddy Campbell,David L. Wehlau
Publisher : American Mathematical Soc.
Page : 308 pages
File Size : 47,6 Mb
Release : 2024-07-03
Category : Science
ISBN : 0821870300

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Invariant Theory in All Characteristics by Harold Edward Alexander Eddy Campbell,David L. Wehlau Pdf

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.

Author : Mara D. Neusel
Publisher : American Mathematical Soc.
Page : 326 pages
File Size : 43,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821841327

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Invariant Theory by Mara D. Neusel Pdf

This book presents the characteristic zero invariant theory of finite groups acting linearly on polynomial algebras. The author assumes basic knowledge of groups and rings, and introduces more advanced methods from commutative algebra along the way. The theory is illustrated by numerous examples and applications to physics, engineering, numerical analysis, combinatorics, coding theory, and graph theory. A wide selection of exercises and suggestions for further reading makes the book appropriate for an advanced undergraduate or first-year graduate level course.

Author : Mara D. Neusel,Larry Smith
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 49,5 Mb
Release : 2010-03-08
Category : Mathematics
ISBN : 9780821849811

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Invariant Theory of Finite Groups by Mara D. Neusel,Larry Smith Pdf

The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods and tools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invariant theory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, additional problems appear and are compensated for in part by the emergence of new tools. One of these is the Steenrod algebra, which the authors introduce in Chapter 8 to solve the inverse invariant theory problem, around which the authors have organized the last three chapters. The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader with orientation to the vast literature.

Author : T.A. Springer
Publisher : Springer
Page : 118 pages
File Size : 40,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540373704

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Invariant Theory by T.A. Springer Pdf

Author : Corrado De Concini,Claudio Procesi
Publisher : American Mathematical Soc.
Page : 153 pages
File Size : 45,9 Mb
Release : 2017-11-16
Category : Invariants
ISBN : 9781470441876

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The Invariant Theory of Matrices by Corrado De Concini,Claudio Procesi Pdf

This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving (1) the first fundamental theorem that describes a set of generators in the ring of invariants, and (2) the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.

Author : John Fogarty
Publisher : Unknown
Page : 240 pages
File Size : 49,7 Mb
Release : 1969
Category : Mathematics
ISBN : UOM:39015049069365

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Invariant Theory by John Fogarty Pdf

Author : Igor Dolgachev
Publisher : Cambridge University Press
Page : 244 pages
File Size : 41,6 Mb
Release : 2003-08-07
Category : Mathematics
ISBN : 0521525489

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Lectures on Invariant Theory by Igor Dolgachev Pdf

The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

Author : Peter J. Olver
Publisher : Cambridge University Press
Page : 308 pages
File Size : 48,5 Mb
Release : 1999-01-13
Category : Mathematics
ISBN : 0521558212

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Classical Invariant Theory by Peter J. Olver Pdf

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

Author : H.E.A. Eddy Campbell,David L. Wehlau
Publisher : Springer Science & Business Media
Page : 233 pages
File Size : 42,9 Mb
Release : 2011-01-12
Category : Mathematics
ISBN : 9783642174049

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Modular Invariant Theory by H.E.A. Eddy Campbell,David L. Wehlau Pdf

This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the better understood non-modular setting. It details techniques for the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers—an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter.

Author : Jean Alexandre Dieudonné,Jean Dieudonné,James B. Carrell
Publisher : Unknown
Page : 104 pages
File Size : 45,7 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015015622759

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Invariant Theory, Old and New by Jean Alexandre Dieudonné,Jean Dieudonné,James B. Carrell Pdf

Author : Shigeru Mukai
Publisher : Cambridge University Press
Page : 528 pages
File Size : 49,7 Mb
Release : 2003-09-08
Category : Mathematics
ISBN : 0521809061

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An Introduction to Invariants and Moduli by Shigeru Mukai Pdf

Sample Text

Author : H.E.A. Eddy Campbell,David Wehlau
Publisher : Springer
Page : 234 pages
File Size : 50,7 Mb
Release : 2011-04-08
Category : Mathematics
ISBN : 3642174051

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Modular Invariant Theory by H.E.A. Eddy Campbell,David Wehlau Pdf

This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the better understood non-modular setting. It details techniques for the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers—an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter.

Author : David J. Benson
Publisher : Unknown
Page : 130 pages
File Size : 53,6 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107362032

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Polynomial Invariants of Finite Groups by David J. Benson Pdf

This is the first book to deal with invariant theory and the representations of finite groups. By restricting attention to finite groups Dr Benson is able to avoid recourse to the technical machinery of algebraic groups, and he develops the necessary results from commutative algebra as he proceeds. Thus the book should be accessible to graduate students. In detail, the book contains an account of invariant theory for the action of a finite group on the ring of polynomial functions on a linear representation, both in characteristic zero and characteristic p. Special attention is paid to the role played by pseudoreflections, which arise because they correspond to the divisors in the polynomial ring which ramify over the invariants. Also included is a new proof by Crawley-Boevey and the author of the Carlisle-Kropholler conjecture. This volume will appeal to all algebraists, but especially those working in representation theory, group theory, and commutative or homological algebra.

Author : Martin Lorenz
Publisher : Springer Science & Business Media
Page : 179 pages
File Size : 50,5 Mb
Release : 2005-12-08
Category : Mathematics
ISBN : 9783540273585

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Multiplicative Invariant Theory by Martin Lorenz Pdf

Multiplicative invariant theory, as a research area in its own right within the wider spectrum of invariant theory, is of relatively recent vintage. The present text offers a coherent account of the basic results achieved thus far.. Multiplicative invariant theory is intimately tied to integral representations of finite groups. Therefore, the field has a predominantly discrete, algebraic flavor. Geometry, specifically the theory of algebraic groups, enters through Weyl groups and their root lattices as well as via character lattices of algebraic tori. Throughout the text, numerous explicit examples of multiplicative invariant algebras and fields are presented, including the complete list of all multiplicative invariant algebras for lattices of rank 2. The book is intended for graduate and postgraduate students as well as researchers in integral representation theory, commutative algebra and, mostly, invariant theory.