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Author : David Hilbert
Publisher : Cambridge University Press
Page : 212 pages
File Size : 52,5 Mb
Release : 1993-11-26
Category : Mathematics
ISBN : 0521449030
An English translation of the notes from David Hilbert's course in 1897 on Invariant Theory at the University of Gottingen taken by his student Sophus Marxen.
Author : David Hilbert
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 52,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662035450
A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.
Author : Igor Dolgachev
Publisher : Cambridge University Press
Page : 244 pages
File Size : 41,5 Mb
Release : 2003-08-07
Category : Mathematics
ISBN : 0521525489
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 : T.A. Springer
Publisher : Springer
Page : 118 pages
File Size : 55,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540373704
Author : Jean Alexandre Dieudonné,Jean Dieudonné,James B. Carrell
Publisher : Unknown
Page : 104 pages
File Size : 43,9 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015058207716
Author : Frank D. Grosshans
Publisher : Springer
Page : 158 pages
File Size : 43,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540696179
The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. This book is an exposition of several related topics including observable subgroups, induced modules, maximal unipotent subgroups of reductive groups and the method of U-invariants, and the complexity of an action. Much of this material has not appeared previously in book form. The exposition assumes a basic knowledge of algebraic groups and then develops each topic systematically with applications to invariant theory. Exercises are included as well as many examples, some of which are related to geometry and physics.
Author : H.E.A. Eddy Campbell,David L. Wehlau
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 46,8 Mb
Release : 2011-01-12
Category : Mathematics
ISBN : 9783642174049
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 : Peter J. Olver
Publisher : Cambridge University Press
Page : 308 pages
File Size : 42,7 Mb
Release : 1999-01-13
Category : Mathematics
ISBN : 0521558212
The book is a self-contained introduction to the results and methods in classical invariant theory.
Author : Martin Lorenz
Publisher : Springer Science & Business Media
Page : 179 pages
File Size : 50,6 Mb
Release : 2005-12-08
Category : Mathematics
ISBN : 9783540273585
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.
Author : John Fogarty
Publisher : Unknown
Page : 240 pages
File Size : 55,9 Mb
Release : 1969
Category : Mathematics
ISBN : UOM:39015049069365
Author : Mara D. Neusel,Larry Smith
Publisher : American Mathematical Soc.
Page : 371 pages
File Size : 50,9 Mb
Release : 2010-03-08
Category : Mathematics
ISBN : 9780821849811
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 : John Hilton Grace,Alfred Young
Publisher : Cambridge University Press
Page : 400 pages
File Size : 43,5 Mb
Release : 2010-10-31
Category : History
ISBN : 9781108013093
This 1903 book, which became a standard work, made recent German research on invariant theory available to British mathematicians.
Author : Marcos Marino,Michael Thaddeus,Ravi Vakil
Publisher : Springer
Page : 210 pages
File Size : 43,5 Mb
Release : 2008-08-15
Category : Mathematics
ISBN : 9783540798149
Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.
Author : Walter Ricardo Ferrer Santos,Alvaro Rittatore
Publisher : CRC Press
Page : 479 pages
File Size : 53,8 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9781482239164
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.
Author : Mara D. Neusel
Publisher : American Mathematical Soc.
Page : 326 pages
File Size : 49,5 Mb
Release : 2007
Category : Invariants
ISBN : 9780821841327
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.