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Infinite dimensional Lie algebras

Author: Victor G Kac
Publisher: Cambridge ; New York : Cambridge University Press, [1995] ©1990
Edition/Format:   Print book : English : Third edition, reprinted with correctionsView all editions and formats
Database:WorldCat
Summary:
The third, substantially revised edition of a monograph concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie albegras, and their representations, based on courses given over a number of years at MIT and in Paris.
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Document Type: Book
All Authors / Contributors: Victor G Kac
ISBN: 0521466938 9780521466936
OCLC Number: 40398125
Description: xxi, 400 p. ; 24 cm
Contents: Basic definitions --
The invariant bilinear form and the generalized Casimir operator --
Integrable representations of Kac-Moody algebras and the Weyl group --
A classification of generalized Cartan matrices --
Real and imaginary roots --
Affine algebras: the normalized invariant form, the root system, and the Weyl group --
Affine algebras as central extensions of loop algebras --
Twisted affine algebras and finite order automorphisms --
Highest-weight modules over Kac-Moody algebras --
Integrable highest-weight modules: the character formula --
Integrable highest-weight modules: the weight system and the unitarizability --
Integrable highest-weight modules over affine algebras. Application to n-function identities. Sugawara operators and branching functions --
Affine algebras, theta functions, and modular forms --
The principle and homogeneous vertex operator constructions of the basic representation. Boson-Fermion correspondence. Application to Soliton equations.
Responsibility: Victor G. Kac.

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This is the third, substantially revised edition of this important monograph and graduate text.  Read more...

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'A clear account of Kac-Moody algebras by one of the founders ... Eminently suitable as an introduction ... with a surprising number of exercises.' American Mathematical Monthly ' ... a useful Read more...

 
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