Invariant Theory Of Finite Groups PDF Download
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Author | : Mara D. Neusel |
Publisher | : American Mathematical Soc. |
Total Pages | : 384 |
Release | : 2010-03-08 |
Genre | : Mathematics |
ISBN | : 0821849816 |
Download Invariant Theory of Finite Groups Book in PDF, ePub and Kindle
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 | : D. J. Benson |
Publisher | : Cambridge University Press |
Total Pages | : 134 |
Release | : 1993-10-07 |
Genre | : Mathematics |
ISBN | : 9780521458863 |
Download Polynomial Invariants of Finite Groups Book in PDF, ePub and Kindle
This is the first book to deal with invariant theory and the representations of finite groups.
Author | : H.E.A. Eddy Campbell |
Publisher | : Springer Science & Business Media |
Total Pages | : 233 |
Release | : 2011-01-12 |
Genre | : Mathematics |
ISBN | : 3642174043 |
Download Modular Invariant Theory Book in PDF, ePub and Kindle
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 | : Bernd Sturmfels |
Publisher | : Springer Science & Business Media |
Total Pages | : 202 |
Release | : 2008-06-17 |
Genre | : Mathematics |
ISBN | : 3211774173 |
Download Algorithms in Invariant Theory Book in PDF, ePub and Kindle
This book is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to research ideas, hints for applications, outlines and details of algorithms, examples and problems.
Author | : Mara D. Neusel |
Publisher | : American Mathematical Soc. |
Total Pages | : 326 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821841327 |
Download Invariant Theory Book in PDF, ePub and Kindle
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 | : T.A. Springer |
Publisher | : Springer |
Total Pages | : 118 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540373705 |
Download Invariant Theory Book in PDF, ePub and Kindle
Author | : Harm Derksen |
Publisher | : Springer Science & Business Media |
Total Pages | : 272 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662049589 |
Download Computational Invariant Theory Book in PDF, ePub and Kindle
This book, the first volume of a subseries on "Invariant Theory and Algebraic Transformation Groups", provides a comprehensive and up-to-date overview of the algorithmic aspects of invariant theory. Numerous illustrative examples and a careful selection of proofs make the book accessible to non-specialists.
Author | : Richard Kane |
Publisher | : Springer Science & Business Media |
Total Pages | : 382 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475735421 |
Download Reflection Groups and Invariant Theory Book in PDF, ePub and Kindle
Reflection groups and invariant theory is a branch of mathematics that lies at the intersection between geometry and algebra. The book contains a deep and elegant theory, evolved from various graduate courses given by the author over the past 10 years.
Author | : David J. Benson |
Publisher | : |
Total Pages | : 130 |
Release | : 2014-05-14 |
Genre | : MATHEMATICS |
ISBN | : 9781107362031 |
Download Polynomial Invariants of Finite Groups Book in PDF, ePub and Kindle
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 | : Igor Dolgachev |
Publisher | : Cambridge University Press |
Total Pages | : 244 |
Release | : 2003-08-07 |
Genre | : Mathematics |
ISBN | : 9780521525480 |
Download Lectures on Invariant Theory Book in PDF, ePub and Kindle
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.