Algorithms In Invariant Theory
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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 | : 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 | : Gabriele Nebe |
Publisher | : Springer Science & Business Media |
Total Pages | : 474 |
Release | : 2006-02-09 |
Genre | : Mathematics |
ISBN | : 9783540307297 |
Download Self-Dual Codes and Invariant Theory Book in PDF, Epub and Kindle
One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory, which has inspired hundreds of papers about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations.
Author | : David Cox |
Publisher | : Springer Science & Business Media |
Total Pages | : 523 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475721811 |
Download Ideals, Varieties, and Algorithms Book in PDF, Epub and Kindle
Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.
Author | : Look Kwang Wong |
Publisher | : |
Total Pages | : 82 |
Release | : 1998 |
Genre | : Algorithms |
ISBN | : |
Download Algorithms in Invariant Theory Book in PDF, Epub and Kindle
Author | : Peter J. Olver |
Publisher | : Cambridge University Press |
Total Pages | : 308 |
Release | : 1999-01-13 |
Genre | : Mathematics |
ISBN | : 9780521558211 |
Download Classical Invariant Theory Book in PDF, Epub and Kindle
The book is a self-contained introduction to the results and methods in classical invariant theory.
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.
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 | : Frank D. Grosshans |
Publisher | : American Mathematical Soc. |
Total Pages | : 106 |
Release | : 1987-12-31 |
Genre | : Mathematics |
ISBN | : 0821807196 |
Download Invariant Theory and Superalgebras Book in PDF, Epub and Kindle
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.
Author | : Martin Lorenz |
Publisher | : Springer Science & Business Media |
Total Pages | : 179 |
Release | : 2005-12-08 |
Genre | : Mathematics |
ISBN | : 3540273581 |
Download Multiplicative Invariant Theory Book in PDF, Epub and Kindle
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.