The Geometry of Infinite-Dimensional Groups

Author: Boris Khesin,Robert Wendt

Publisher: Springer Science & Business Media

ISBN: 3540772634

Category: Mathematics

Page: 304

View: 577

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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.
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Representations of Infinite-dimensional Groups

Author: Rais Salmanovich Ismagilov

Publisher: American Mathematical Soc.

ISBN: 9780821897683

Category: Mathematics

Page: 197

View: 512

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This book is devoted to representations of two classes of infinite-dimensional groups: current groups and diffeomorphism groups. The author presents a complete treatment of the subject, including general methods for constructing irreducible representations of infinite-dimensional groups and general results about such representations. He also exhibits deep relations between representations of infinite-dimensional grops and the theory of Fock spaces, the theory of point random processes, and other branches of mathematics.
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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: 1767

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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:
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Infinite Dimensional Groups with Applications

Author: Victor Kac

Publisher: Springer Science & Business Media

ISBN: 1461211042

Category: Mathematics

Page: 380

View: 6402

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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.
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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: 3467

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

Author: Marion Jean,Heyer Herbert

Publisher: World Scientific

ISBN: 9814544841

Category:

Page: 408

View: 6312

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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.
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Infinite Dimensional Kähler Manifolds

Author: Alan Huckleberry,Tilmann Wurzbacher

Publisher: Springer Science & Business Media

ISBN: 9783764366025

Category: Mathematics

Page: 375

View: 9933

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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.
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Dynamics of Infinite-dimensional Groups

The Ramsey-Dvoretzky-Milman Phenomenon

Author: Vladimir Pestov

Publisher: American Mathematical Soc.

ISBN: 9780821882962

Category: Mathematics

Page: 192

View: 2360

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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.
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Infinite-dimensional Lie Groups. General Theory and Main Examples

Author: Helge Glöckner,Karl-Hermann Neeb

Publisher: Springer

ISBN: 9780387094441

Category: Mathematics

Page: 350

View: 9595

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Provides a comprehensive introduction to this important subject, examining the basic structure theory of infinite-dimensional Lie groups Essentially self-contained, provides all necessary background, excepting modest prerequisites Clear exposition includes careful explanations, illustrative examples, numerous exercises, and detailed cross-references to simplify a non-linear reading of the material
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Handbook of the Geometry of Banach Spaces

Author: William B. Johnson,Joram Lindenstrauss

Publisher: Elsevier

ISBN: 9780444513052

Category: Mathematics

Page: 1866

View: 6690

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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.
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