Group Actions And Invariant Theory

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Group Actions and Invariant Theory

Author : Andrzej Białynicki-Birula
Publisher : American Mathematical Soc.
ISBN 13 : 9780821860151
Total Pages : 244 pages
Book Rating : 4.8/5 (61 download)

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Book Synopsis Group Actions and Invariant Theory by : Andrzej Białynicki-Birula

Download or read book Group Actions and Invariant Theory written by Andrzej Białynicki-Birula and published by American Mathematical Soc.. This book was released on 1989 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a conference, sponsored by the Canadian Mathematical Society, on Group Actions and Invariant Theory, held in August, 1988 in Montreal. The conference was the third in a series bringing together researchers from North America and Europe (particularly Poland). The papers collected here will provide an overview of the state of the art of research in this area. The conference was primarily concerned with the geometric side of invariant theory, including explorations of the linearization problem for reductive group actions on affine spaces (with a counterexample given recently by J. Schwarz), spherical and complete symmetric varieties, reductive quotients, automorphisms of affine varieties, and homogeneous vector bundles.

Group Actions on Rings

Author : Susan Montgomery
Publisher : American Mathematical Soc.
ISBN 13 : 0821850466
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Group Actions on Rings by : Susan Montgomery

Download or read book Group Actions on Rings written by Susan Montgomery and published by American Mathematical Soc.. This book was released on 1985 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ring theorists and researchers in invariant theory and operator algebra met at Bowdoin for the 1984 AMS-IMS-SIAM Joint Summer Research Conference to exchange ideas about group actions on rings. This work discusses topics common to the three fields, including: $K$-theory, dual actions, semi-invariants and crossed products.

Actions and Invariants of Algebraic Groups

Author : Walter Ricardo Ferrer Santos
Publisher : CRC Press
ISBN 13 : 1482239167
Total Pages : 479 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Actions and Invariants of Algebraic Groups by : Walter Ricardo Ferrer Santos

Download or read book Actions and Invariants of Algebraic Groups written by Walter Ricardo Ferrer Santos and published by CRC Press. This book was released on 2017-09-19 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on Invariant Theory

Author : Igor Dolgachev
Publisher : Cambridge University Press
ISBN 13 : 9780521525480
Total Pages : 244 pages
Book Rating : 4.5/5 (254 download)

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Book Synopsis Lectures on Invariant Theory by : Igor Dolgachev

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.

An Introduction to Invariants and Moduli

Author : Shigeru Mukai
Publisher : Cambridge University Press
ISBN 13 : 9780521809061
Total Pages : 528 pages
Book Rating : 4.8/5 (9 download)

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Book Synopsis An Introduction to Invariants and Moduli by : Shigeru Mukai

Download or read book An Introduction to Invariants and Moduli written by Shigeru Mukai and published by Cambridge University Press. This book was released on 2003-09-08 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample Text

Algorithms in Invariant Theory

Author : Bernd Sturmfels
Publisher : Springer Science & Business Media
ISBN 13 : 3211774173
Total Pages : 202 pages
Book Rating : 4.2/5 (117 download)

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Book Synopsis Algorithms in Invariant Theory by : Bernd Sturmfels

Download or read book Algorithms in Invariant Theory written by Bernd Sturmfels and published by Springer Science & Business Media. This book was released on 2008-06-17 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Group actions and invariant theory

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 9780821860151
Total Pages : 228 pages
Book Rating : 4.8/5 (61 download)

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Book Synopsis Group actions and invariant theory by :

Download or read book Group actions and invariant theory written by and published by American Mathematical Soc.. This book was released on 1989 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Reflection Groups and Invariant Theory

Author : Richard Kane
Publisher : Springer Science & Business Media
ISBN 13 : 1475735421
Total Pages : 382 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Reflection Groups and Invariant Theory by : Richard Kane

Download or read book Reflection Groups and Invariant Theory written by Richard Kane and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflection groups and invariant theory is a branch of mathematics that lies at the intersection between geometry and algebra. The book contains a deep and elegant theory, evolved from various graduate courses given by the author over the past 10 years.

Algebraic Homogeneous Spaces and Invariant Theory

Author : Frank D. Grosshans
Publisher : Springer
ISBN 13 : 3540696172
Total Pages : 158 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Algebraic Homogeneous Spaces and Invariant Theory by : Frank D. Grosshans

Download or read book Algebraic Homogeneous Spaces and Invariant Theory written by Frank D. Grosshans and published by Springer. This book was released on 2006-11-14 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Symmetry, Representations, and Invariants

Author : Roe Goodman
Publisher : Springer Science & Business Media
ISBN 13 : 0387798528
Total Pages : 731 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Symmetry, Representations, and Invariants by : Roe Goodman

Download or read book Symmetry, Representations, and Invariants written by Roe Goodman and published by Springer Science & Business Media. This book was released on 2009-07-30 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Invariant Theory of Finite Groups

Author : Mara D. Neusel
Publisher : American Mathematical Soc.
ISBN 13 : 0821849816
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Invariant Theory of Finite Groups by : Mara D. Neusel

Download or read book Invariant Theory of Finite Groups written by Mara D. Neusel and published by American Mathematical Soc.. This book was released on 2010-03-08 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computational Invariant Theory

Author : Harm Derksen
Publisher : Springer Science & Business Media
ISBN 13 : 3662049589
Total Pages : 272 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Computational Invariant Theory by : Harm Derksen

Download or read book Computational Invariant Theory written by Harm Derksen and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Invariant Theory

Author : Sebastian S. Koh
Publisher : Springer
ISBN 13 : 3540479082
Total Pages : 111 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Invariant Theory by : Sebastian S. Koh

Download or read book Invariant Theory written by Sebastian S. Koh and published by Springer. This book was released on 2006-11-15 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Invariant Theory in All Characteristics

Author : Harold Edward Alexander Eddy Campbell
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870303
Total Pages : 308 pages
Book Rating : 4.8/5 (73 download)

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Book Synopsis Invariant Theory in All Characteristics by : Harold Edward Alexander Eddy Campbell

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.

Actions and Invariants of Algebraic Groups

Author : Walter Ricardo Ferrer Santos
Publisher : CRC Press
ISBN 13 : 1351644777
Total Pages : 709 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Actions and Invariants of Algebraic Groups by : Walter Ricardo Ferrer Santos

Download or read book Actions and Invariants of Algebraic Groups written by Walter Ricardo Ferrer Santos and published by CRC Press. This book was released on 2017-09-19 with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Reflection Groups and Invariant Theory

Author : Richard Kane
Publisher : Springer Science & Business Media
ISBN 13 : 9780387989792
Total Pages : 664 pages
Book Rating : 4.9/5 (897 download)

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Book Synopsis Reflection Groups and Invariant Theory by : Richard Kane

Download or read book Reflection Groups and Invariant Theory written by Richard Kane and published by Springer Science & Business Media. This book was released on 2001-06-21 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflection groups and invariant theory is a branch of mathematics that lies at the intersection between geometry and algebra. The book contains a deep and elegant theory, evolved from various graduate courses given by the author over the past 10 years.

Multiplicative Invariant Theory

Author : Martin Lorenz
Publisher : Springer Science & Business Media
ISBN 13 : 3540273581
Total Pages : 179 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Multiplicative Invariant Theory by : Martin Lorenz

Download or read book Multiplicative Invariant Theory written by Martin Lorenz and published by Springer Science & Business Media. This book was released on 2005-12-08 with total page 179 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.