The Geometry of Infinite-Dimensional Groups

Author: Boris Khesin,Robert Wendt

Publisher: Springer Science & Business Media

ISBN: 3540772634

Category: Mathematics

Page: 304

View: 6966

This monograph gives an overview of various classes of infinite-dimensional Lie groups and their applications in Hamiltonian mechanics, fluid dynamics, integrable systems, gauge theory, and complex geometry. The text includes many exercises and open questions.

Infinite Dimensional Lie Groups in Geometry and Representation Theory

Author: Augustin Banyaga,Joshua A Leslie,Thierry Robart

Publisher: World Scientific

ISBN: 9814488143

Category: Science

Page: 176

View: 6578

This book constitutes the proceedings of the 2000 Howard conference on “Infinite Dimensional Lie Groups in Geometry and Representation Theory”. It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and established researchers in the field of geometry and its applications to mathematical physics. Contents:Inheritance Properties for Lipschitz-Metrizable Frölicher Groups (J Teichmann)Around the Exponential Mapping (T Robart)On a Solution to a Global Inverse Problem with Respect to Certain Generalized Symmetrizable Kac-Moody Algebras (J A Leslie)The Lie Group of Fourier Integral Operators on Open Manifolds (R Schmid)On Some Properties of Leibniz Algebroids (A Wade)On the Geometry of Locally Conformal Symplectic Manifolds (A Banyaga)Some Properties of Locally Conformal Symplectic Manifolds (S Haller)Criticality of Unit Contact Vector Fields (P Rukimbira)Orbifold Homeomorphism and Diffeomorphism Groups (J E Borzellino & V Brunsden)A Note on Isotopies of Symplectic and Poisson Structures (A Banyaga & P Donato)Remarks on Actions on Compacta by Some Infinite-Dimensional Groups (V Pestov) Readership: Graduate students and researchers in mathematics and mathematical physics. Keywords:

Infinite Dimensional Groups and Manifolds

Author: Tilmann Wurzbacher

Publisher: Walter de Gruyter

ISBN: 3110200015

Category: Mathematics

Page: 256

View: 9555

Dieser Band beinhaltet eine Sammlung wissenschaftlicher Forschungsbeiträge zu unendlich-dimensionalen Gruppen und Mannigfaltigkeiten in der Mathematik und Quantenphysik.

Infinite Dimensional Groups with Applications

Author: Victor Kac

Publisher: Springer Science & Business Media

ISBN: 1461211042

Category: Mathematics

Page: 380

View: 3219

This volume records most of the talks given at the Conference on Infinite-dimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10-May 15, 1984, as a part of the special program on Kac-Moody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinite-dimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general Kac-Moody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my thanks to the MSRI for sponsoring the meeting, to Ms. Faye Yeager for excellent typing, to the authors for their manuscripts, and to Springer-Verlag for publishing this volume. V. Kac INFINITE DIMENSIONAL GROUPS WITH APPLICATIONS CONTENTS The Lie Group Structure of M. Adams. T. Ratiu 1 Diffeomorphism Groups and & R. Schmid Invertible Fourier Integral Operators with Applications On Landau-Lifshitz Equation and E. Date 71 Infinite Dimensional Groups Flat Manifolds and Infinite D. S. Freed 83 Dimensional Kahler Geometry Positive-Energy Representations R. Goodman 125 of the Group of Diffeomorphisms of the Circle Instantons and Harmonic Maps M. A. Guest 137 A Coxeter Group Approach to Z. Haddad 157 Schubert Varieties Constructing Groups Associated to V. G. Kac 167 Infinite-Dimensional Lie Algebras I. Kaplansky 217 Harish-Chandra Modules Over the Virasoro Algebra & L. J. Santharoubane 233 Rational Homotopy Theory of Flag S.

Analysis On Infinite-dimensional Lie Groups And Algebras - Proceedings Of The International Colloquium

Author: Marion Jean,Heyer Herbert

Publisher: World Scientific

ISBN: 9814544841


Page: 408

View: 5649

The book provides a comprehensive “map” of China's financial markets and institutions based on objective data. The book uses the mentioned data to analyze the status and trend of China's financial sectors under macro-economy. The objective of this book is to show the actual performance of China's financial markets and institutions during the first stage of the post-crisis period and the challenges that China's financial sectors face in the future.At present, China's economy and financial sectors are just like a traveler undergoing a long journey and need a map to tell where he/she comes from, where he/she is and where the present road will lead to. This book attempts to provide the readers with some useful information on the basis of objective data and help them to explore the road to the near future of China's economy and financial sectors.

Developments and Trends in Infinite-Dimensional Lie Theory

Author: Karl-Hermann Neeb,Arturo Pianzola

Publisher: Springer Science & Business Media

ISBN: 9780817647414

Category: Mathematics

Page: 492

View: 6663

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.

Infinite Dimensional Kähler Manifolds

Author: Alan Huckleberry,Tilmann Wurzbacher

Publisher: Birkhäuser

ISBN: 3034882270

Category: Mathematics

Page: 375

View: 7136

Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold.

Handbook of the Geometry of Banach Spaces

Author: William B. Johnson,Joram Lindenstrauss

Publisher: Elsevier

ISBN: 9780444513052

Category: Mathematics

Page: 1866

View: 5897

Encouraged by new perspectives in Banach space theory, the editors present this second volume that opens with an introductory essay that explains the basics of the theory. The rest of the chapters focus on specific directions of Banach space theory or its applications.

Differential Analysis in Infinite Dimensional Spaces

Proceedings of an AMS Special Session Held August 8-10, 1983, with Partial Support from the NSERC (Canada)

Author: Kondagunta Sundaresan

Publisher: American Mathematical Soc.

ISBN: 0821850598

Category: Mathematics

Page: 122

View: 5790

This volume focuses on developments made in the past two decades in the field of differential analysis in infinite dimensional spaces. New techniques such as ultraproducts and ultrapowers have illuminated the relationship between the geometric properties of Banach spaces and the existence of differentiable functions on the spaces. The wide range of topics covered also includes gauge theories, polar subsets, approximation theory, group analysis of partial differential equations, inequalities, and actions on infinite groups. Addressed to both the expert and the advanced graduate student, the book requires a basic knowledge of functional analysis and differential topology.

The Geometry of Physics

An Introduction

Author: Frankel Theodore

Publisher: 清华大学出版社有限公司

ISBN: 9787302073512

Category: Geometry, Differential

Page: 694

View: 4241

Lie Theory

Lie Algebras and Representations

Author: Jens Carsten Jantzen,Jean-Philippe Anker,Karl-Hermann Neeb,Bent Orsted

Publisher: Springer Science & Business Media

ISBN: 9780817633738

Category: Mathematics

Page: 328

View: 5374

* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.

Symmetries and Overdetermined Systems of Partial Differential Equations

Author: Michael Eastwood,Willard Miller

Publisher: Springer Science & Business Media

ISBN: 9780387738314

Category: Mathematics

Page: 568

View: 5322

This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.

Geometry of Foliations

Author: Philippe Tondeur

Publisher: Springer Science & Business Media

ISBN: 9783764357412

Category: Mathematics

Page: 305

View: 1337

This volume describes research on the differential geometry of foliations, in particular Riemannian foliations, done over the last few years. It can be read by graduate students and researchers with a background in differential geometry and Riemannian geometry. Of particular interest will be the Hodge theory for the transversal Laplacian, and applications of the heat equation method to Riemannian foliations. There are chapters on the spectral theory for Riemannian foliations, on Connes' point of view of foliations as examples of noncommutative spaces, and a chapter on infinite-dimensional examples of Riemannian foliations.

Dynamics of Infinite-dimensional Groups

The Ramsey-Dvoretzky-Milman Phenomenon

Author: Vladimir Pestov

Publisher: American Mathematical Soc.

ISBN: 9780821882962

Category: Mathematics

Page: 192

View: 7459

The ''infinite-dimensional groups'' in the title refer to unitary groups of Hilbert spaces, the infinite symmetric group, groups of homeomorphisms of manifolds, groups of transformations of measure spaces, etc. The book presents an approach to the study of such groups based on ideas from geometric functional analysis and from exploring the interplay between dynamical properties of those groups, combinatorial Ramsey-type theorems, and the phenomenon of concentration of measure. Thedynamics of infinite-dimensional groups is very much unlike that of locally compact groups. For instance, every locally compact group acts freely on a suitable compact space (Veech). By contrast, a 1983 result by Gromov and Milman states that whenever the unitary group of a separable Hilbert spacecontinuously acts on a compact space, it has a common fixed point. In the book, this new fast-growing theory is built strictly from well-understood examples up. The book has no close counterpart and is based on recent research articles. At the same time, it is organized so as to be reasonably self-contained. The topic is essentially interdisciplinary and will be of interest to mathematicians working in geometric functional analysis, topological and ergodic dynamics, Ramsey theory, logic anddescriptive set theory, representation theory, topological groups, and operator algebras.

Geometry of Quantum Theory

Author: V.S. Varadarajan

Publisher: Springer Science & Business Media

ISBN: 0387493867

Category: Science

Page: 412

View: 864

Available for the first time in soft cover, this book is a classic on the foundations of quantum theory. It examines the subject from a point of view that goes back to Heisenberg and Dirac and whose definitive mathematical formulation is due to von Neumann. This view leads most naturally to the fundamental questions that are at the basis of all attempts to understand the world of atomic and subatomic particles.

Infinite-dimensional Lie Groups

Author: N.A

Publisher: American Mathematical Soc.

ISBN: 9780821889589

Category: Mathematics

Page: 415

View: 1065

This book develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinite-dimensional Lie groups all the real, primitive, infinite transformation groups studied by E. Cartan. The book discusses several noncommutative algebras such as Weyl algebras and algebras of quantum groups and their automorphism groups. The notion of a noncommutative manifold is described, and the deformation quantization of certain algebras is discussed from the viewpoint of Lie algebras. This edition is a revised version of the book of the same title published in Japanese in 1979.

From Geometry to Quantum Mechanics

In Honor of Hideki Omori

Author: Yoshiaki Maeda,Peter Michor,Takushiro Ochiai,Akira Yoshioka

Publisher: Springer Science & Business Media

ISBN: 0817645306

Category: Mathematics

Page: 324

View: 6471

* Invited articles in differential geometry and mathematical physics in honor of Hideki Omori * Focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, Lie group theory, quantizations and noncommutative geometry, as well as applications of PDEs and variational methods to geometry * Will appeal to graduate students in mathematics and quantum mechanics; also a reference

Geometry of Classical Fields

Author: E. Binz,J. Sniatycki,H.R. Fischer

Publisher: Elsevier

ISBN: 9780080872650

Category: Mathematics

Page: 447

View: 7157

This volume is an introduction to differential methods in physics. Part I contains a comprehensive presentation of the geometry of manifolds and Lie groups, including infinite dimensional settings. The differential geometric notions introduced in Part I are used in Part II to develop selected topics in field theory, from the basic principles up to the present state of the art. This second part is a systematic development of a covariant Hamiltonian formulation of field theory starting from the principle of stationary action.