
Current Algebras and Groups
Jouko Mickelsson(Author)
Springer (Publisher)
Published on 3. March 2013
Book
Paperback/Softback
XVII, 313 pages
978-1-4757-0297-2 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1989
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
XVII, 313 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 19 mm
Weight
505 gr
ISBN-13
978-1-4757-0297-2 (9781475702972)
DOI
10.1007/978-1-4757-0295-8
Schweitzer Classification
Other editions
Additional editions

Jouko Mickelsson
Current Algebras and Groups
Book
12/1989
Kluwer Academic / Plenum Publishers
€85.55
Article exhausted; check different version
Content
1 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.