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Lie Algebras, Part 2: Volume 7 Finite and Infinite Dimensional Lie Algebras and Applications in Physics(Volume 7 Studies in Mathematical Physics)

Lie Algebras, Part 2: Volume 7 Finite and Infinite Dimensional Lie Algebras and Applications in Physics(Volume 7 Studies in Mathematical Physics)

          
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About the Book

This is the follow-up to "Lie Algebras Part 1", which covered a major part of the theory of Kac-Moody algebras, stressing primarily their mathematical structure. Part two deals mainly with the representations and applications of lie algebras, and contains many cross-references to "Part 1". The exposition of the theory of Kac-Moody algebras is continued in this volume, starting with an explicit construction of (untwisted) affine Kac-Moody algebras as extensions of loop algebras by a central element and a derivation. Three chapters deal with the representation theory of Kac-Moody algebras and some of the concepts are developed in a more general context, namely that of algebras with a triangular decomposition, of which Kac-Moody algebras are special examples. The basic notion of the representation theory of lie algebras with a triangular decomposition, namely that of a highest weight representation is also dealt with. Integrable highest weight representations are treated in a further chapter, along with the generalized Casimir operator, the standard and grand unified models of elementary particle physics, the theory of soliton equations and the realm of 2D conformal field theory.

Table of Contents:
Preface. 18. Extensions of Lie algebras. 19. Explicit construction of affine Kac-Moody algebras. 20. Representations - enveloping algebra techniques. 21. The Weyl group and integrable representations. 22. More on representations. 23. Characters and multiplicities. 24. Quarks, leptons and gauge fields. 25. Lie algebras of infinite matrices. 26. Representations of loop algebras. 27. KP-hierarchies. 28. Conformal symmetry.


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Product Details
  • ISBN-13: 9780444828361
  • Publisher: Elsevier Science & Technology
  • Publisher Imprint: North-Holland
  • Language: English
  • Series Title: Volume 7 Studies in Mathematical Physics
  • Weight: 1000 gr
  • ISBN-10: 0444828362
  • Publisher Date: 30 Oct 1997
  • Binding: Hardback
  • No of Pages: 553
  • Sub Title: Volume 7 Finite and Infinite Dimensional Lie Algebras and Applications in Physics


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Lie Algebras, Part 2: Volume 7 Finite and Infinite Dimensional Lie Algebras and Applications in Physics(Volume 7 Studies in Mathematical Physics)
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