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Algebraic Homogeneous Spaces And Invariant Theory
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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.
Book Synopsis Homogeneous Spaces and Equivariant Embeddings by : D.A. Timashev
Download or read book Homogeneous Spaces and Equivariant Embeddings written by D.A. Timashev and published by Springer Science & Business Media. This book was released on 2011-04-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory. By standard reasons of algebraic geometry, in order to solve various problems on a homogeneous space, it is natural and helpful to compactify it while keeping track of the group action, i.e., to consider equivariant completions or, more generally, open embeddings of a given homogeneous space. Such equivariant embeddings are the subject of this book. We focus on the classification of equivariant embeddings in terms of certain data of "combinatorial" nature (the Luna-Vust theory) and description of various geometric and representation-theoretic properties of these varieties based on these data. The class of spherical varieties, intensively studied during the last three decades, is of special interest in the scope of this book. Spherical varieties include many classical examples, such as Grassmannians, flag varieties, and varieties of quadrics, as well as well-known toric varieties. We have attempted to cover most of the important issues, including the recent substantial progress obtained in and around the theory of spherical varieties.
Book Synopsis Projective Duality and Homogeneous Spaces by : Evgueni A. Tevelev
Download or read book Projective Duality and Homogeneous Spaces written by Evgueni A. Tevelev and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Projective duality is a very classical notion naturally arising in various areas of mathematics, such as algebraic and differential geometry, combinatorics, topology, analytical mechanics, and invariant theory, and the results in this field were until now scattered across the literature. Thus the appearance of a book specifically devoted to projective duality is a long-awaited and welcome event. Projective Duality and Homogeneous Spaces covers a vast and diverse range of topics in the field of dual varieties, ranging from differential geometry to Mori theory and from topology to the theory of algebras. It gives a very readable and thorough account and the presentation of the material is clear and convincing. For the most part of the book the only prerequisites are basic algebra and algebraic geometry. This book will be of great interest to graduate and postgraduate students as well as professional mathematicians working in algebra, geometry and analysis.
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.
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 542 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.
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.
Book Synopsis Lie Groups and Invariant Theory by : Ėrnest Borisovich Vinberg
Download or read book Lie Groups and Invariant Theory written by Ėrnest Borisovich Vinberg and published by American Mathematical Soc.. This book was released on 2005 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, devoted to the 70th birthday of A. L. Onishchik, contains a collection of articles by participants in the Moscow Seminar on Lie Groups and Invariant Theory headed by E. B. Vinberg and A. L. Onishchik. The book is suitable for graduate students and researchers interested in Lie groups and related topics.
Book Synopsis Invariant Theory, Old and New by : Jean Alexandre Dieudonné
Download or read book Invariant Theory, Old and New written by Jean Alexandre Dieudonné and published by . This book was released on 1971 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 :Harold Edward Alexander Eddy Campbell Publisher :American Mathematical Soc. ISBN 13 :9780821870303 Total Pages :308 pages Book Rating :4.8/5 (73 download)
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.
Book Synopsis Invariance and System Theory by : Allen Tannenbaum
Download or read book Invariance and System Theory written by Allen Tannenbaum and published by Springer. This book was released on 2006-11-14 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Lie Groups, Their Discrete Subgroups, and Invariant Theory by : Ėrnest Borisovich Vinberg
Download or read book Lie Groups, Their Discrete Subgroups, and Invariant Theory written by Ėrnest Borisovich Vinberg and published by American Mathematical Society(RI). This book was released on 1992 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the past thirty years, E B Vinberg and L A Onishchik have conducted a seminar on Lie groups at Moscow University; about five years ago V L Popov became the third co-director, and the range of topics expanded to include invariant theory. Today, the seminar encompasses such areas as algebraic groups, geometry and topology of homogeneous spaces, and Kac-Moody groups and algebras. This collection presents a snapshot of the research activities of this well-established seminar, including new results in Lie groups, crystallographic groups, and algebraic transformation groups. These papers will not be published elsewhere. Readers will find this volume useful for the new results it contains as well as for the open problems it poses.
Book Synopsis An Introduction to Lie Groups and the Geometry of Homogeneous Spaces by : Andreas Arvanitogeōrgos
Download or read book An Introduction to Lie Groups and the Geometry of Homogeneous Spaces written by Andreas Arvanitogeōrgos and published by American Mathematical Soc.. This book was released on 2003 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the reader started. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of other topics. Lie groups and homogeneous spaces are especially useful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The book is suitable for advanced undergraduates, graduate students, and research mathematicians interested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics.
Book Synopsis Torsors, Étale Homotopy and Applications to Rational Points by : Alexei Skorobogatov
Download or read book Torsors, Étale Homotopy and Applications to Rational Points written by Alexei Skorobogatov and published by . This book was released on 2013 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Torsors, also known as principal bundles or principal homogeneous spaces, are ubiquitous in mathematics. The purpose of this book is to present expository lecture notes and cutting-edge research papers on the theory and applications of torsors and étale homotopy, all written from different perspectives by leading experts. Part one of the book contains lecture notes on recent uses of torsors in geometric invariant theory and representation theory, plus an introduction to the étale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the étale homotopy approach to the arithmetic of rational points. Furthermore, the reader will find a collection of research articles on algebraic groups and homogeneous spaces, rational and K3 surfaces, geometric invariant theory, rational points, descent and the Brauer-Manin obstruction. Together, these give a state-of-the-art view of a broad area at the crossroads of number theory and algebraic geometry.
Book Synopsis Algebraic Geometry IV by : A.N. Parshin
Download or read book Algebraic Geometry IV written by A.N. Parshin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
