Invariant Theory And Superalgebras

Author : Frank D. Grosshans,Gian-Carlo Rota,Joel A. Stein
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 51,8 Mb
Release : 1987-12-31
Category : Mathematics
ISBN : 9780821807194

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Invariant Theory and Superalgebras by Frank D. Grosshans,Gian-Carlo Rota,Joel A. Stein Pdf

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 : Peter J. Olver
Publisher : Cambridge University Press
Page : 308 pages
File Size : 45,9 Mb
Release : 1999-01-13
Category : Mathematics
ISBN : 0521558212

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Classical Invariant Theory by Peter J. Olver Pdf

The book is a self-contained introduction to the results and methods in classical invariant theory.

Author : T.A. Springer
Publisher : Springer
Page : 118 pages
File Size : 51,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540373704

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Invariant Theory by T.A. Springer Pdf

Author : Maria Gorelik,Vladimir Hinich,Anna Melnikov
Publisher : Springer Nature
Page : 553 pages
File Size : 47,5 Mb
Release : 2019-10-18
Category : Mathematics
ISBN : 9783030235314

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Representations and Nilpotent Orbits of Lie Algebraic Systems by Maria Gorelik,Vladimir Hinich,Anna Melnikov Pdf

This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.

Author : Jean Alexandre Dieudonné,Jean Dieudonné,James B. Carrell
Publisher : Unknown
Page : 104 pages
File Size : 42,5 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015058207716

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Invariant Theory, Old and New by Jean Alexandre Dieudonné,Jean Dieudonné,James B. Carrell Pdf

Author : Mara D. Neusel
Publisher : American Mathematical Soc.
Page : 326 pages
File Size : 50,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821841327

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Invariant Theory by Mara D. Neusel Pdf

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 : Frank D. Grosshans
Publisher : Springer
Page : 158 pages
File Size : 47,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540696179

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Algebraic Homogeneous Spaces and Invariant Theory by Frank D. Grosshans Pdf

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 : Roe Goodman,Nolan R. Wallach
Publisher : Springer Science & Business Media
Page : 731 pages
File Size : 44,8 Mb
Release : 2009-07-30
Category : Mathematics
ISBN : 9780387798523

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Symmetry, Representations, and Invariants by Roe Goodman,Nolan R. Wallach Pdf

Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: (1) Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus; (2) Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux); (3) Self-contained chapters, appendices, comprehensive bibliography; (4) More than 350 exercises (most with detailed hints for solutions) further explore main concepts; (5) Serves as an excellent main text for a one-year course in Lie group theory; (6) Benefits physicists as well as mathematicians as a reference work.

Author : A.N. Parshin,I.R. Shafarevich
Publisher : Springer Science & Business Media
Page : 291 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783662030738

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Algebraic Geometry IV by A.N. Parshin,I.R. Shafarevich Pdf

Two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory, by well-known experts in the fields. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.

Author : Harm Derksen,Gregor Kemper
Publisher : Springer
Page : 366 pages
File Size : 42,7 Mb
Release : 2015-12-23
Category : Mathematics
ISBN : 9783662484227

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Computational Invariant Theory by Harm Derksen,Gregor Kemper Pdf

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 : M. Scheunert
Publisher : Springer
Page : 280 pages
File Size : 42,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540352860

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The Theory of Lie Superalgebras by M. Scheunert Pdf

Author : A. Bialynicki-Birula,J. Carrell,W.M. McGovern
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 51,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662050712

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Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action by A. Bialynicki-Birula,J. Carrell,W.M. McGovern Pdf

This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.

Author : Sebastian S. Koh
Publisher : Springer
Page : 111 pages
File Size : 45,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540479086

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Invariant Theory by Sebastian S. Koh Pdf

This volume of expository papers is the outgrowth of a conference in combinatorics and invariant theory. In recent years, newly developed techniques from algebraic geometry and combinatorics have been applied with great success to some of the outstanding problems of invariant theory, moving it back to the forefront of mathematical research once again. This collection of papers centers on constructive aspects of invariant theory and opens with an introduction to the subject by F. Grosshans. Its purpose is to make the current research more accesssible to mathematicians in related fields.

Author : Harold Edward Alexander Eddy Campbell,David L. Wehlau
Publisher : American Mathematical Soc.
Page : 308 pages
File Size : 47,5 Mb
Release : 2024-07-04
Category : Science
ISBN : 0821870300

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Invariant Theory in All Characteristics by Harold Edward Alexander Eddy Campbell,David L. Wehlau Pdf

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 : Mara D. Neusel,Larry Smith
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 43,7 Mb
Release : 2010-03-08
Category : Mathematics
ISBN : 9780821849811

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Invariant Theory of Finite Groups by Mara D. Neusel,Larry Smith Pdf

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.