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Author: Robert Ellis
Publisher:
Published: 1961
Total Pages: 46
ISBN-13:
DOWNLOAD EBOOKLet T be an abstract group, (beta T, T) the betac mpactificati n of T regarded as a transformation group with phase group T. The collection of all point transitive transformati n groups (X, T) with compact phase space X is studied by representing each such X as a set of homomorphisms of certain subalgebras of C(beta T) into C(beta T). (Author).
Author: Sophus Lie
Publisher: Springer
Published: 2015-03-12
Total Pages: 640
ISBN-13: 3662462117
DOWNLOAD EBOOKThis modern translation of Sophus Lie's and Friedrich Engel's “Theorie der Transformationsgruppen I” will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations and also in physics, for example in general relativity. This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry.
Author:
Publisher: Academic Press
Published: 1972-09-29
Total Pages: 477
ISBN-13: 0080873596
DOWNLOAD EBOOKIntroduction to Compact Transformation Groups
Author: Shoshichi Kobayashi
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 192
ISBN-13: 3642619819
DOWNLOAD EBOOKGiven 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.
Author: A. L. Onishchik
Publisher:
Published: 1994
Total Pages: 324
ISBN-13:
DOWNLOAD EBOOKAuthor: Robert Ellis
Publisher:
Published: 1958
Total Pages: 50
ISBN-13:
DOWNLOAD EBOOKAuthor: John Van Etten Westfall
Publisher:
Published: 1899
Total Pages: 36
ISBN-13:
DOWNLOAD EBOOKAuthor: Deane Montgomery
Publisher: Courier Dover Publications
Published: 2018-06-13
Total Pages: 305
ISBN-13: 0486831582
DOWNLOAD EBOOKAn advanced monograph on the subject of topological transformation groups, this volume summarizes important research conducted during a period of lively activity in this area of mathematics. The book is of particular note because it represents the culmination of research by authors Deane Montgomery and Leo Zippin, undertaken in collaboration with Andrew Gleason of Harvard University, that led to their solution of a well-known mathematical conjecture, Hilbert's Fifth Problem. The treatment begins with an examination of topological spaces and groups and proceeds to locally compact groups and groups with no small subgroups. Subsequent chapters address approximation by Lie groups and transformation groups, concluding with an exploration of compact transformation groups.
Author: Sigurdur Helgason
Publisher: American Mathematical Society
Published: 2024-04-05
Total Pages: 504
ISBN-13: 1470476878
DOWNLOAD EBOOKSigurdur Helgason's Differential Geometry and Symmetric Spaces was quickly recognized as a remarkable and important book. For many years, it was the standard text both for Riemannian geometry and for the analysis and geometry of symmetric spaces. Several generations of mathematicians relied on it for its clarity and careful attention to detail. Although much has happened in the field since the publication of this book, as demonstrated by Helgason's own three-volume expansion of the original work, this single volume is still an excellent overview of the subjects. For instance, even though there are now many competing texts, the chapters on differential geometry and Lie groups continue to be among the best treatments of the subjects available. There is also a well-developed treatment of Cartan's classification and structure theory of symmetric spaces. The last chapter, on functions on symmetric spaces, remains an excellent introduction to the study of spherical functions, the theory of invariant differential operators, and other topics in harmonic analysis. This text is rightly called a classic.
Author: Eldar Straume
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 106
ISBN-13: 082180409X
DOWNLOAD EBOOKThe cohomogeneity of a transformation group ([italic capitals]G, X) is, by definition, the dimension of its orbit space, [italic]c = dim [italic capitals]X, G. By enlarging this simple numerical invariant, but suitably restricted, one gradually increases the complexity of orbit structures of transformation groups. This is a natural program for classical space forms, which traditionally constitute the first canonical family of testing spaces, due to their unique combination of topological simplicity and abundance in varieties of compact differentiable transformation groups.
