Multiplicative Invariant Theory

Author : Martin Lorenz
Publisher : Springer Science & Business Media
ISBN 13 : 9783540243236
Total Pages : 200 pages
Book Rating : 4.32/5 ( download)

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Download or read book Multiplicative Invariant Theory written by Martin Lorenz and published by Springer Science & Business Media. This book was released on 2005-03-10 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jessica Ann Hamm
Publisher :
ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.39/5 ( download)

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Download or read book Multiplicative Invariants of Root Lattices written by Jessica Ann Hamm and published by . This book was released on 2014 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical invariant theory is a field of study within abstract algebra that has been around for well over a century. However, the field of multiplicative invariant theory is rather new, having only been studied formally for the past 35 years. Multiplicative invariants arise naturally in a variety of settings, notably as representation rings of Lie algebras, centers of group algebras, and actions on algebraic tori. In this thesis we calculate the multiplicative invariants for lattices associated to root systems under the actions of their Weyl groups.

Author : T.A. Springer
Publisher : Springer
ISBN 13 : 3540373705
Total Pages : 118 pages
Book Rating : 4.04/5 ( download)

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Download or read book Invariant Theory written by T.A. Springer and published by Springer. This book was released on 2006-11-14 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Mohammed S. Tesemma
Publisher :
ISBN 13 :
Total Pages : 122 pages
Book Rating : 4.47/5 ( download)

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Download or read book Reflection Groups and Semigroup Algebras in Multiplicative Invariant Theory written by Mohammed S. Tesemma and published by . This book was released on 2004 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Harold Edward Alexander Eddy Campbell
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870303
Total Pages : 308 pages
Book Rating : 4.00/5 ( download)

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Download or read book Invariant Theory in All Characteristics written by Harold Edward Alexander Eddy Campbell and published by American Mathematical Soc.. This book was released on with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Harm Derksen
Publisher : Springer
ISBN 13 : 3662484226
Total Pages : 387 pages
Book Rating : 4.27/5 ( download)

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Download or read book Computational Invariant Theory written by Harm Derksen and published by Springer. This book was released on 2015-12-23 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Igor Dolgachev
Publisher : Cambridge University Press
ISBN 13 : 9780521525480
Total Pages : 244 pages
Book Rating : 4.89/5 ( download)

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Download or read book Lectures on Invariant Theory written by Igor Dolgachev and published by Cambridge University Press. This book was released on 2003-08-07 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
ISBN 13 : 9780821841327
Total Pages : 314 pages
Book Rating : 4.27/5 ( download)

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Download or read book Invariant Theory written by Mara D. Neusel and published by American Mathematical Soc.. This book was released on 2007 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Scott Chapman
Publisher : Springer
ISBN 13 : 9783319388533
Total Pages : 0 pages
Book Rating : 4.33/5 ( download)

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Download or read book Multiplicative Ideal Theory and Factorization Theory written by Scott Chapman and published by Springer. This book was released on 2016-07-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.

Author : H.E.A. Eddy Campbell
Publisher : Springer Science & Business Media
ISBN 13 : 3642174043
Total Pages : 233 pages
Book Rating : 4.49/5 ( download)

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Download or read book Modular Invariant Theory written by H.E.A. Eddy Campbell and published by Springer Science & Business Media. This book was released on 2011-01-12 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.