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Algebraic Transformation Groups and Algebraic Varieties
Author: Vladimir Leonidovich Popov
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 244
ISBN-13: 3662056526
DOWNLOAD EBOOK →The book covers topics in the theory of algebraic transformation groups and algebraic varieties which are very much at the frontier of mathematical research.
Transformation Groups and Algebraic K-Theory
Author: Wolfgang Lück
Publisher: Springer
Published: 2006-11-14
Total Pages: 455
ISBN-13: 3540468277
DOWNLOAD EBOOK →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.
Algebraic Transformation Groups and Algebraic Varieties
Author: Vladimir Leonidovich Popov
Publisher: Springer
Published: 2014-01-15
Total Pages: 252
ISBN-13: 9783662056530
DOWNLOAD EBOOK →Topological Methods in Algebraic Transformation Groups
Author: Kraft
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 216
ISBN-13: 1461237025
DOWNLOAD EBOOK →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.
Topological Methods in Algebraic Transformation Groups
Author: 3Island Press
Publisher:
Published: 1990-01-01
Total Pages: 224
ISBN-13: 9781461237037
DOWNLOAD EBOOK →Transformation Groups in Differential Geometry
Author: Shoshichi Kobayashi
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 192
ISBN-13: 3642619819
DOWNLOAD EBOOK →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.
Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action
Author: A. Bialynicki-Birula
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 248
ISBN-13: 3662050714
DOWNLOAD EBOOK →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.
Transformation Groups and Lie Algebras
Author: Nail H Ibragimov
Publisher: World Scientific Publishing Company
Published: 2013-05-20
Total Pages: 196
ISBN-13: 9814460869
DOWNLOAD EBOOK →This book is based on the extensive experience of teaching for mathematics, physics and engineering students in Russia, USA, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics. The methods of local Lie groups discussed in the book provide universal and effective method for solving nonlinear differential equations analytically. Introduction to approximate transformation groups also contained in the book helps to develop skills in constructing approximate solutions for differential equations with a small parameter.
Representations of Fundamental Groups of Algebraic Varieties
Author: Kang Zuo
Publisher: Springer
Published: 2006-11-14
Total Pages: 142
ISBN-13: 3540484248
DOWNLOAD EBOOK →Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.
