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

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

Author: Jean Marion

Publisher: World Scientific

Published: 1998-10-30

Total Pages: 410

ISBN-13: 9814544841

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This proceedings volume can be considered as a monograph on the state-of-the-art in the wide range of analysis on infinite-dimensional algebraic-topological structures. Topics covered in this volume include integrability and regularity for Lie groups and Lie algebras, actions of infinite-dimensional Lie groups on manifolds of paths and related minimal orbits, quasi-invariant measures, white noise analysis, harmonic analysis on generalized convolution structures, and noncommutative geometry. A special feature of this volume is the interrelationship between problems of pure and applied mathematics and also between mathematics and physics.

The Convenient Setting of Global Analysis

The Convenient Setting of Global Analysis PDF

Author: Andreas Kriegl

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 631

ISBN-13: 0821807803

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For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR

Infinite Dimensional Lie Groups In Geometry And Representation Theory

Infinite Dimensional Lie Groups In Geometry And Representation Theory PDF

Author: Augustin Banyaga

Publisher: World Scientific

Published: 2002-07-12

Total Pages: 174

ISBN-13: 9814488143

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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.

An Introduction to Infinite-Dimensional Differential Geometry

An Introduction to Infinite-Dimensional Differential Geometry PDF

Author: Alexander Schmeding

Publisher: Cambridge University Press

Published: 2022-12-22

Total Pages: 284

ISBN-13: 1009089307

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Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core.

Infinite-Dimensional Lie Groups

Infinite-Dimensional Lie Groups PDF

Author: Hideki Omori

Publisher: American Mathematical Soc.

Published: 2017-11-07

Total Pages: 415

ISBN-13: 1470426358

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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.