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Mantles, Trains and Representations of Infinite Dimensional Groups

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First European Congress of Mathematics Paris, July 6–10, 1992

Part of the book series: Progress in Mathematics ((PM,volume 120))

Abstract

The term “infinite dimensional group” is heuristic. It does not have a rigid definition. The most interesting types of groups which might be considered as infinite dimensional groups are:

  • groups of diffeomorphisms of manifolds;

  • the group of diffeomorphisms of a circle (it is the exceptional case among other groups of diffeomorphisms);

  • groups corresponding to Kac-Moody algebras;

  • infinite dimensional analogues of classical groups;

  • infinite analogues of symmetric groups;

  • current groups (i.e., groups of functions on some set X with values in fixed groups G);

  • groups of transformations of spaces with measure.

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Author information

Authors and Affiliations

  1. Novozavodskaya 25/11-6-27, Moscow, 121309, Russia

    Yurii A. Neretin

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  1. Yurii A. Neretin
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Editors and Affiliations

  1. Laboratoire de Mathématiques Fondamentales, Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris Cedex 05, France

    Anthony Joseph  & Rudolf Rentschler  & 

  2. The Weizmann Institute of Science, Rehovot, 76100, Israel

    Anthony Joseph

  3. Mathématiques, Université de Paris-Sud, Bâtiment 425, 91405, Orsay Cedex, France

    Fulbert Mignot

  4. Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, 4, place Jussieu, 75252, Paris Cedex 05, France

    François Murat

  5. Laboratoire de Statistique Médicale, Université Paris V, 45, rue des Saints Pères, 75270, Paris Cedex 06, France

    Bernard Prum

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© 1994 Birkhäuser Verlag

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Neretin, Y.A. (1994). Mantles, Trains and Representations of Infinite Dimensional Groups. In: Joseph, A., Mignot, F., Murat, F., Prum, B., Rentschler, R. (eds) First European Congress of Mathematics Paris, July 6–10, 1992. Progress in Mathematics, vol 120. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9112-7_12

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  • DOI: https://doi.org/10.1007/978-3-0348-9112-7_12

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9912-3

  • Online ISBN: 978-3-0348-9112-7

  • eBook Packages: Springer Book Archive

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