Download or read book Algebraic Transformation Groups and Algebraic Varieties written by Vladimir Leonidovich Popov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers topics in the theory of algebraic transformation groups and algebraic varieties which are very much at the frontier of mathematical research.
Download or read book Transformation Groups and Algebraic K Theory written by Wolfgang Lück and published by Springer. This book was released on 2006-11-14 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic K-theory of modules over a category is studied extensively and appplied to the fundamental category of G-space. Basic details of the theory of transformation groups sometimes hard to find in the literature, are collected here (Chapter I) for the benefit of graduate students. Chapters II and III contain advanced new material of interest to researchers working in transformation groups, algebraic K-theory or related fields.
Download or read book Transformation Groups written by Tammo tom Dieck and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: “This book is a jewel – it explains important, useful and deep topics in Algebraic Topology that you won’t find elsewhere, carefully and in detail.” Prof. Günter M. Ziegler, TU Berlin
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.
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.
Download or read book Algebraic Varieties written by G. Kempf and published by Cambridge University Press. This book was released on 1993-09-09 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.
Download or read book The Art of Doing Algebraic Geometry written by Thomas Dedieu and published by Springer Nature. This book was released on 2023-04-14 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state of the art of the covered topics and reflecting the versatility of the scientific interests of Ciro Ciliberto.
Download or read book Linear Algebraic Groups written by Armand Borel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised, enlarged edition of Linear Algebraic Groups (1969) starts by presenting foundational material on algebraic groups, Lie algebras, transformation spaces, and quotient spaces. It then turns to solvable groups, general properties of linear algebraic groups, and Chevally’s structure theory of reductive groups over algebraically closed groundfields. It closes with a focus on rationality questions over non-algebraically closed fields.
Download or read book Algebraic Groups written by J. S. Milne and published by Cambridge University Press. This book was released on 2017-09-21 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive introduction to the theory of algebraic group schemes over fields, based on modern algebraic geometry, with few prerequisites.
Download or read book Lie Groups and Algebraic Groups written by Arkadij L. Onishchik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the notes of the authors' seminar on algebraic and Lie groups held at the Department of Mechanics and Mathematics of Moscow University in 1967/68. Our guiding idea was to present in the most economic way the theory of semisimple Lie groups on the basis of the theory of algebraic groups. Our main sources were A. Borel's paper [34], C. ChevalIey's seminar [14], seminar "Sophus Lie" [15] and monographs by C. Chevalley [4], N. Jacobson [9] and J-P. Serre [16, 17]. In preparing this book we have completely rearranged these notes and added two new chapters: "Lie groups" and "Real semisimple Lie groups". Several traditional topics of Lie algebra theory, however, are left entirely disregarded, e.g. universal enveloping algebras, characters of linear representations and (co)homology of Lie algebras. A distinctive feature of this book is that almost all the material is presented as a sequence of problems, as it had been in the first draft of the seminar's notes. We believe that solving these problems may help the reader to feel the seminar's atmosphere and master the theory. Nevertheless, all the non-trivial ideas, and sometimes solutions, are contained in hints given at the end of each section. The proofs of certain theorems, which we consider more difficult, are given directly in the main text. The book also contains exercises, the majority of which are an essential complement to the main contents.
Download or read book Rational Points on Varieties written by Bjorn Poonen and published by American Mathematical Soc.. This book was released on 2017-12-13 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Download or read book Transformation Groups for Beginners written by Sergeĭ Vasilʹevich Duzhin and published by American Mathematical Soc.. This book was released on 2004 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a discussion of algebraic operations on the points in the plane and rigid motions in the Euclidean plane. This work introduces the notions of a transformation group and of an abstract group. It gives an elementary exposition of the basic ideas of Sophus Lie about symmetries of differential equations.
Download or read book Topological Methods in Algebraic Transformation Groups written by Hanspeter Kraft and published by Springer Science & Business Media. This book was released on 1990 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, there has been increasing interest and activity in the area of group actions on affine and projective algebraic varieties. Tech niques from various branches of mathematics have been important for this study, especially those coming from the well-developed theory of smooth compact transformation groups. It was timely to have an interdisciplinary meeting on these topics. We organized the conference "Topological Methods in Alg~braic Transformation Groups," which was held at Rutgers University, 4-8 April, 1988. Our aim was to facilitate an exchange of ideas and techniques among mathematicians studying compact smooth transformation groups, alge braic transformation groups and related issues in algebraic and analytic geometry. The meeting was well attended, and these Proceedings offer a larger audience the opportunity to benefit from the excellent survey and specialized talks presented. The main topics concerned various as pects of group actions, algebraic quotients, homogeneous spaces and their compactifications. The meeting was made possible by support from Rutgers University and the National Science Foundation. We express our deep appreciation for this support. We also thank Annette Neuen for her assistance with the technical preparation of these Proceedings.
Download or read book Algebraic Quotients Torus Actions and Cohomology The Adjoint Representation and the Adjoint Action written by A. Bialynicki-Birula and published by Springer Science & Business Media. This book was released on 2002-04-24 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Transformation Groups in Differential Geometry written by Shoshichi Kobayashi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.
Download or read book Cohomological Methods in Transformation Groups written by C. Allday and published by Cambridge University Press. This book was released on 1993-07 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.
