Progress in Mathematics

Developments and Trends in Infinite-Dimensional Lie Theory

Editors: Neeb, Karl-Hermann, Pianzola, Arturo (Eds.)

  • 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
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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.

Table of contents (14 chapters)

  • Isotopy for Extended Affine Lie Algebras and Lie Tori

    Allison, Bruce (et al.)

    Pages 3-43

  • Remarks on the Isotriviality of Multiloop Algebras

    Gille, Philippe (et al.)

    Pages 45-51

  • Extended Affine Lie Algebras and Other Generalizations of Affine Lie Algebras – A Survey

    Neher, Erhard

    Pages 53-126

  • Tensor Representations of Classical Locally Finite Lie Algebras

    Penkov, Ivan (et al.)

    Pages 127-150

  • Lie Algebras, Vertex Algebras, and Automorphic Forms

    Scheithauer, Nils R.

    Pages 151-168

Buy this book

eBook $159.00
price for USA (gross)
  • ISBN 978-0-8176-4741-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $209.00
price for USA
  • ISBN 978-0-8176-4740-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Developments and Trends in Infinite-Dimensional Lie Theory
Editors
  • Karl-Hermann Neeb
  • Arturo Pianzola
Series Title
Progress in Mathematics
Series Volume
288
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-8176-4741-4
DOI
10.1007/978-0-8176-4741-4
Hardcover ISBN
978-0-8176-4740-7
Series ISSN
0743-1643
Edition Number
1
Number of Pages
VIII, 492
Number of Illustrations and Tables
9 b/w illustrations
Topics