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OverviewLet 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. Full Product DetailsAuthor: Jouko MickelssonPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 1989 Dimensions: Width: 15.50cm , Height: 1.80cm , Length: 23.50cm Weight: 0.510kg ISBN: 9781475702972ISBN 10: 1475702973 Pages: 313 Publication Date: 03 March 2013 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1 Semisimple Lie Algebras.- 2 Representations of Affine Kac-Moody Algebras.- 3 Principal Bundles.- 4 Extensions of Groups of Gauge Transformations.- 5 The Chiral Anomaly.- 6 Determinant Bundles Over Grassmannians.- 7 The Virasoro Algebra.- 8 The Boson Fermion Correspondence.- 9 Holomorphic Aspects of String Theory.- 10 The Nonlinear ? Model.- 11 The KP Hierarchy.- 12 The Fock Bundle of a Dirac Operator and Infinite Grassmannians.- References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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