Actions And Invariants Of Algebraic Groups

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Actions and Invariants of Algebraic Groups

Walter Ricardo Ferrer Santos,Alvaro Rittatore
Actions and Invariants of Algebraic Groups Book PDF

Author : Walter Ricardo Ferrer Santos,Alvaro Rittatore
Publisher : CRC Press
Page : 479 pages
File Size : 45,7 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9781482239164

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Actions and Invariants of Algebraic Groups by Walter Ricardo Ferrer Santos,Alvaro Rittatore Pdf

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.

Actions and Invariants of Algebraic Groups, Second Edition

Walter Ricardo Ferrer Santos
Actions and Invariants of Algebraic Groups Second Edition Book PDF

Author : Walter Ricardo Ferrer Santos
Publisher : Unknown
Page : 472 pages
File Size : 53,6 Mb
Release : 2017
Category : Affine algebraic groups
ISBN : 0429135734

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Actions and Invariants of Algebraic Groups, Second Edition by Walter Ricardo Ferrer Santos Pdf

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.--Provided by publisher.

Actions and Invariants of Algebraic Groups

Walter Ferrer Santos,Alvaro Rittatore
Actions and Invariants of Algebraic Groups Book PDF

Author : Walter Ferrer Santos,Alvaro Rittatore
Publisher : CRC Press
Page : 472 pages
File Size : 40,9 Mb
Release : 2005-04-26
Category : Mathematics
ISBN : 9781420030792

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Actions and Invariants of Algebraic Groups by Walter Ferrer Santos,Alvaro Rittatore Pdf

Actions and Invariants of Algebraic Groups presents a self-contained introduction to geometric invariant theory that links the basic theory of affine algebraic groups to Mumford's more sophisticated theory. The authors systematically exploit the viewpoint of Hopf algebra theory and the theory of comodules to simplify and compactify many of the rele

Group Actions and Invariant Theory

Andrzej Białynicki-Birula
Group Actions and Invariant Theory Book PDF

Author : Andrzej Białynicki-Birula
Publisher : American Mathematical Soc.
Page : 244 pages
File Size : 45,6 Mb
Release : 1989
Category : Mathematics
ISBN : 0821860151

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Group Actions and Invariant Theory by Andrzej Białynicki-Birula Pdf

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.

Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action

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

Author : A. Bialynicki-Birula,J. Carrell,W.M. McGovern
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 43,8 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.

Algebraic Homogeneous Spaces and Invariant Theory

Frank D. Grosshans
Algebraic Homogeneous Spaces and Invariant Theory Book PDF

Author : Frank D. Grosshans
Publisher : Springer
Page : 158 pages
File Size : 44,7 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.

Lectures on Invariant Theory

Igor Dolgachev
Lectures on Invariant Theory Book PDF

Author : Igor Dolgachev
Publisher : Cambridge University Press
Page : 244 pages
File Size : 50,9 Mb
Release : 2003-08-07
Category : Mathematics
ISBN : 0521525489

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Lectures on Invariant Theory by Igor Dolgachev Pdf

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.

Algebraic Geometry IV

A.N. Parshin,I.R. Shafarevich
Algebraic Geometry IV Book PDF

Author : A.N. Parshin,I.R. Shafarevich
Publisher : Springer Science & Business Media
Page : 291 pages
File Size : 51,7 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.

Group Actions on Rings

Susan Montgomery
Group Actions on Rings Book PDF

Author : Susan Montgomery
Publisher : American Mathematical Soc.
Page : 277 pages
File Size : 41,7 Mb
Release : 1985
Category : Mathematics
ISBN : 9780821850466

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Group Actions on Rings by Susan Montgomery Pdf

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.

Symmetry, Representations, and Invariants

Roe Goodman,Nolan R. Wallach
Symmetry Representations and Invariants Book PDF

Author : Roe Goodman,Nolan R. Wallach
Publisher : Springer Science & Business Media
Page : 731 pages
File Size : 49,5 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.

Algebraic Groups and Their Birational Invariants

V. E. Voskresenskii,V. E. VoskresenskiuI and Boris Kunyavski
Algebraic Groups and Their Birational Invariants Book PDF

Author : V. E. Voskresenskii,V. E. VoskresenskiuI and Boris Kunyavski
Publisher : American Mathematical Soc.
Page : 234 pages
File Size : 46,6 Mb
Release : 2011-10-06
Category : Mathematics
ISBN : 9780821872888

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Algebraic Groups and Their Birational Invariants by V. E. Voskresenskii,V. E. VoskresenskiuI and Boris Kunyavski Pdf

Since the late 1960s, methods of birational geometry have been used successfully in the theory of linear algebraic groups, especially in arithmetic problems. This book--which can be viewed as a significant revision of the author's book, Algebraic Tori (Nauka, Moscow, 1977)--studies birational properties of linear algebraic groups focusing on arithmetic applications. The main topics are forms and Galois cohomology, the Picard group and the Brauer group, birational geometry of algebraic tori, arithmetic of algebraic groups, Tamagawa numbers, $R$-equivalence, projective toric varieties, invariants of finite transformation groups, and index-formulas. Results and applications are recent. There is an extensive bibliography with additional comments that can serve as a guide for further reading.

An Introduction to Invariants and Moduli

Shigeru Mukai
An Introduction to Invariants and Moduli Book PDF

Author : Shigeru Mukai
Publisher : Cambridge University Press
Page : 528 pages
File Size : 40,7 Mb
Release : 2003-09-08
Category : Mathematics
ISBN : 0521809061

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An Introduction to Invariants and Moduli by Shigeru Mukai Pdf

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Algebraic Groups: Structure and Actions

Mahir Bilen Can
Algebraic Groups Structure and Actions Book PDF

Author : Mahir Bilen Can
Publisher : American Mathematical Soc.
Page : 294 pages
File Size : 54,5 Mb
Release : 2017-04-06
Category : Algebraic geometry -- Algebraic groups -- Group schemes
ISBN : 9781470426019

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Algebraic Groups: Structure and Actions by Mahir Bilen Can Pdf

This volume contains the proceedings of the 2015 Clifford Lectures on Algebraic Groups: Structures and Actions, held from March 2–5, 2015, at Tulane University, New Orleans, Louisiana. This volume consists of six articles on algebraic groups, including an enhanced exposition of the classical results of Chevalley and Rosenlicht on the structure of algebraic groups; an enhanced survey of the recently developed theory of pseudo-reductive groups; and an exposition of the recently developed operational -theory for singular varieties. In addition, there are three research articles containing previously unpublished foundational results on birational automorphism groups of algebraic varieties; solution of Hermite-Joubert problem over -closed fields; and cohomological invariants and applications to classifying spaces. The old and new results presented in these articles will hopefully become cornerstones for the future development of the theory of algebraic groups and applications. Graduate students and researchers working in the fields of algebraic geometry, number theory, and representation theory will benefit from this unique and broad compilation of fundamental results on algebraic group theory.

Geometric Invariant Theory

David Mumford,John Fogarty,Frances Kirwan
Geometric Invariant Theory Book PDF

Author : David Mumford,John Fogarty,Frances Kirwan
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 42,9 Mb
Release : 1994
Category : Mathematics
ISBN : 3540569634

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Geometric Invariant Theory by David Mumford,John Fogarty,Frances Kirwan Pdf

"Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in 1965, a second, enlarged editonappeared in 1982) is the standard reference on applicationsof invariant theory to the construction of moduli spaces.This third, revised edition has been long awaited for by themathematical community. It is now appearing in a completelyupdated and enlarged version with an additional chapter onthe moment map by Prof. Frances Kirwan (Oxford) and a fullyupdated bibliography of work in this area.The book deals firstly with actions of algebraic groups onalgebraic varieties, separating orbits by invariants andconstructionquotient spaces; and secondly with applicationsof this theory to the construction of moduli spaces.It is a systematic exposition of the geometric aspects ofthe classical theory of polynomial invariants.

Geometric Invariant Theory

Nolan R. Wallach
Geometric Invariant Theory Book PDF

Author : Nolan R. Wallach
Publisher : Springer
Page : 190 pages
File Size : 52,6 Mb
Release : 2017-09-08
Category : Mathematics
ISBN : 9783319659077

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Geometric Invariant Theory by Nolan R. Wallach Pdf

Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough background theory included to make the text accessible to advanced graduate students in mathematics and physics with diverse backgrounds in algebraic and differential geometry. Throughout the book, examples are emphasized. Exercises add to the reader’s understanding of the material; most are enhanced with hints. The exposition is divided into two parts. The first part, ‘Background Theory’, is organized as a reference for the rest of the book. It contains two chapters developing material in complex and real algebraic geometry and algebraic groups that are difficult to find in the literature. Chapter 1 emphasizes the relationship between the Zariski topology and the canonical Hausdorff topology of an algebraic variety over the complex numbers. Chapter 2 develops the interaction between Lie groups and algebraic groups. Part 2, ‘Geometric Invariant Theory’ consists of three chapters (3–5). Chapter 3 centers on the Hilbert–Mumford theorem and contains a complete development of the Kempf–Ness theorem and Vindberg’s theory. Chapter 4 studies the orbit structure of a reductive algebraic group on a projective variety emphasizing Kostant’s theory. The final chapter studies the extension of classical invariant theory to products of classical groups emphasizing recent applications of the theory to physics.