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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Let M be a smooth manifold and G a Lie group. In this book we shall study infinite-dimensional Lie algebras associated both to the group Map(M, G) of smooth mappings from M to G and to the group of dif feomorphisms of M. In the former case the Lie algebra of the group is the algebra Mg of smooth mappings from M to the Lie algebra gof G. In the latter case the Lie algebra is the algebra Vect M of smooth vector fields on M. However, it turns out that in many applications to field theory and statistical physics one must deal with certain extensions of the above mentioned Lie algebras. In the simplest case M is the unit circle SI, G is a simple finite dimensional Lie group and the central extension of Map( SI, g) is an affine Kac-Moody algebra. The highest weight theory of finite dimensional Lie algebras can be extended to the case of an affine Lie algebra. The important point is that Map(Sl, g) can be split to positive and negative Fourier modes and the finite-dimensional piece g corre sponding to the zero mode.
Authors and Affiliations
Bibliographic Information
Book Title: Current Algebras and Groups
Authors: Jouko Mickelsson
Series Title: Plenum Monographs in Nonlinear Physics
DOI: https://doi.org/10.1007/978-1-4757-0295-8
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1989
Softcover ISBN: 978-1-4757-0297-2Published: 03 March 2013
eBook ISBN: 978-1-4757-0295-8Published: 09 March 2013
Edition Number: 1
Number of Pages: XVII, 313