Multiplicative Invariant Theory
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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.
Reflection Groups And Semigroup Algebras In Multiplicative Invariant Theory
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Author : Mohammed S. Tesemma
language : en
Publisher:
Release Date : 2004
Reflection Groups And Semigroup Algebras In Multiplicative Invariant Theory written by Mohammed S. Tesemma and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Algebraic varieties categories.
Multiplicative Invariants Of Root Lattices
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Author : Jessica Ann Hamm
language : en
Publisher:
Release Date : 2014
Multiplicative Invariants Of Root Lattices written by Jessica Ann Hamm and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
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.
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.
Invariant Theory Of Finite Groups
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Author : Mara D. Neusel
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-03-08
Invariant Theory Of Finite Groups 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 2010-03-08 with Mathematics categories.
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.
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.
Invariance And System Theory
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Author : Allen Tannenbaum
language : en
Publisher: Springer
Release Date : 2006-11-14
Invariance And System Theory written by Allen Tannenbaum and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Science categories.
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.
Modular Invariant Theory
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Author : H.E.A. Eddy Campbell
language : en
Publisher: Springer
Release Date : 2011-04-08
Modular Invariant Theory written by H.E.A. Eddy Campbell and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-08 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.
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.