Theory of Transformation Groups I

Theory of Transformation Groups I

This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics.

Author: Sophus Lie

Publisher: Springer

ISBN: 9783662462119

Category: Mathematics

Page: 643

View: 402

This 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.
Categories: Mathematics

Transformation Groups

Transformation Groups

For the representation theory of finite groups. see Serrc [1911] or Curtis-Reiner [I952]; for compact Lie groups, see Briiclter-tom Dicclt [I935]. (2.6) Representation spheres. If a group G acts on a representation space V by orthogonal ...

Author: Tammo tom Dieck

Publisher: Walter de Gruyter

ISBN: 9783110858372

Category: Mathematics

Page: 322

View: 790

“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
Categories: Mathematics

Transformation Groups and Algebraic K Theory

Transformation Groups and Algebraic K Theory

11, 41-46 tom Dieck, T. [1975]: "The Burnside ring of a compact Lie group I", Math. Annalen 215, 235-250 tom Dieck, T. [1979]: "Transformation groups and representation theory", lect. not. in math. 766, Springer tom Dieck, ...

Author: Wolfgang Lück

Publisher: Springer

ISBN: 9783540468271

Category: Mathematics

Page: 454

View: 200

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.
Categories: Mathematics

Theory of Transformation Groups I

Theory of Transformation Groups I

This volume is of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics.

Author: Sophus Lie

Publisher:

ISBN: 3662462125

Category:

Page:

View: 404

This modern translation of Sophus Lie's and Friedrich Engel's "Theorie der Transformationsgruppen Band 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.
Categories:

Developments and Trends in Infinite Dimensional Lie Theory

Developments and Trends in Infinite Dimensional Lie Theory

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics.

Author: Karl-Hermann Neeb

Publisher: Springer Science & Business Media

ISBN: 9780817647414

Category: Mathematics

Page: 492

View: 417

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.
Categories: Mathematics

Developments and Trends in Infinite dimensional Lie Theory Geometry of infinite dimensional lie transformation groups

Developments and Trends in Infinite dimensional Lie Theory  Geometry of infinite dimensional lie  transformation  groups

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics.

Author:

Publisher:

ISBN: 1282973630

Category: Electronic books

Page: 492

View: 312

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super- )algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Part (A) is mainly concerned with the structure and representation theory of infinite-dimensional Lie algebras and contains articles on the structure of direct-limit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and Kac-Moody superalgebras. The articles in Part (B) examine connections between infinite-dimensional Lie theory and geometry. The topics range from infinite-dimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, to Jordan-theoretic geometries and new results on direct-limit groups. The analytic representation theory of infinite-dimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods based on heat kernels, multiplicity freeness, Banach-Lie-Poisson spaces, and infinite-dimensional generalizations of reductive Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.
Categories: Electronic books