Editors:
- Invited papers written by distinguished researchers
- Expository essays focus on recent developments and trends in infinite-dimensional Lie theory
- Discusses new methods, structures, and representations of infinite-dimensional Lie groups
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Mathematics (PM, volume 288)
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Table of contents (14 chapters)
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Front Matter
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Infinite-Dimensional Lie (Super-)Algebras
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Front Matter
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Geometry of Infinite-Dimensional Lie (Transformation) Groups
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Front Matter
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Representation Theory of Infinite-Dimensional Lie Groups
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Front Matter
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Back Matter
About this book
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.
Editors and Affiliations
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Friedrich-Alexander-Universität Erlangen, Department of Mathematics, Erlangen, Germany
Karl-Hermann Neeb
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University of Alberta, Department of Mathematical Sciences, Edmonton, Canada
Arturo Pianzola
Bibliographic Information
Book Title: Developments and Trends in Infinite-Dimensional Lie Theory
Editors: Karl-Hermann Neeb, Arturo Pianzola
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-0-8176-4741-4
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Hardcover ISBN: 978-0-8176-4740-7Published: 28 October 2010
eBook ISBN: 978-0-8176-4741-4Published: 17 October 2010
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: VIII, 492
Number of Illustrations: 9 b/w illustrations
Topics: Topological Groups, Lie Groups, Group Theory and Generalizations, Algebra, Geometry, Algebraic Geometry