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Invariant Theory In All Characteristics

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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.

Invariant Theory In All Characteristics

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Author : Harold Edward Alexander Eddy Campbell
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Lectures On Invariant Theory

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Author : Igor Dolgachev
language : en
Publisher: Cambridge University Press
Release Date : 2003-08-07

Lectures On Invariant Theory written by Igor Dolgachev 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 2003-08-07 with Mathematics categories.

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.

Multiplicative Invariant Theory

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Author : Martin Lorenz
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-03-10

Multiplicative Invariant Theory written by Martin Lorenz 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 2005-03-10 with Mathematics categories.

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.

Modular Invariant Theory

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Author : H.E.A. Eddy Campbell
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-12

Modular Invariant Theory written by H.E.A. Eddy Campbell 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 2011-01-12 with Mathematics categories.

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.

The Invariant Theory Of Matrices

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Author : Corrado De Concini
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-11-16

The Invariant Theory Of Matrices written by Corrado De Concini 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 2017-11-16 with Mathematics categories.

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.

Invariant Theory

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Author : Mara D. Neusel
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Invariant Theory written by Mara D. Neusel 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 2007 with Mathematics categories.

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.

Computational Invariant Theory

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Author : Harm Derksen
language : en
Publisher: Springer
Release Date : 2015-12-23

Computational Invariant Theory written by Harm Derksen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-23 with Mathematics categories.

This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi r Popov, and an addendum by Norbert A'Campo and Vladimir Popov.

Invariant Theory And Superalgebras

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Author : Frank D. Grosshans
language : en
Publisher: American Mathematical Soc.
Release Date : 1987-12-31

Invariant Theory And Superalgebras written by Frank D. Grosshans 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 1987-12-31 with Mathematics categories.

This book brings the reader to the frontiers of research in some topics in superalgebras and symbolic method in invariant theory. Superalgebras are algebras containing positively-signed and negatively-signed variables. One of the book's major results is an extension of the standard basis theorem to superalgebras. This extension requires a rethinking of some basic concepts of linear algebra, such as matrices and coordinate systems, and may lead to an extension of the entire apparatus of linear algebra to ``signed'' modules. The authors also present the symbolic method for the invariant theory of symmetric and of skew-symmetric tensors. In both cases, the invariants are obtained from the symbolic representation by applying what the authors call the umbral operator. This operator can be used to systematically develop anticommutative analogs of concepts of algebraic geometry, and such results may ultimately turn out to be the main byproduct of this investigation. While it will be of special interest to mathematicians and physicists doing research in superalgebras, invariant theory, straightening algorithms, Young bitableaux, and Grassmann's calculus of extension, the book starts from basic principles and should therefore be accessible to those who have completed the standard graduate level courses in algebra and/or combinatorics.

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.

Invariant Theory In All Characteristics

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