http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Supersymmetries and infinite-dimensional algebras
Recent devopments, particularly in high-energy physics, have projected group theory and symmetry consideration into a central position in theoretical physics. These developments have taken physicists increasingly deeper into the fascinating world of pure mathematics. This work presents important mathematical developments of the last fifteen years in a form that is easy to comprehend and appreciate.
Front Cover; Supersymmetries and Infinite-Dimensional Algebras; Copyright Page; Preface; Table of Contents; Contents of Volume I; Contents of Volume II; Part D: Lie Superalgebras, Lie Supergroups and their Applications; Chapter 20. Introduction to Superalgebras and Supermatrices; 1 The notion of grading; 2 Associative superalgebras; 3 Grassmann algebras; 4 Supermatrices; Chapter 21. General Properties of Lie Superalgebras; 1 Lie superalgebras introduced; 2 Definitions and immediate consequences; 3 Subalgebras, direct sums and homomorphisms of Lie superalgebras.
4 Graded representations of Lie superalgebras5 The adjoint representation and the Killing form of a Lie superalgebra; Chapter 22. Superspace and Lie Supergroups; 1 Grassmann variables as coordinates; 2 Analysis on superspace; 3 Linear Lie supergroups; Chapter 23. The Poincaré Superalgebras and Supergroups; 1 Introduction; 2 The N = 1, D = 4 Poincaré superalgebra and supergroup; 3 Extended Poincaré superalgebras and Poincaré supergroups for D = 4; 4 The Poincaré superalgebras and supergroups for Minkowski space-times of general dimension D.
5 Irreducible representations of the unextended D = 4 Poincaré superalgebra6 Irreducible representations of the extended D = 4 Poincaré superalgebras; 7 Irreducible representations of the Poincaré superalgebras for general space-time dimensions; Chapter 24. Poincaré Supersymmetric Fields; 1 Supersymmetric field theory; 2 Supersymmetric multiplets; 3 Superfields; 4 Supersymmetric gauge theories; 5 Spontaneous symmetry breaking; Chapter 25. Simple Lie Superalgebras; 1 An outline of the presentation; 2 The definition of a simple Lie superalgebra and some immediate consequences.
3 Classical simple Lie superalgebras4 Graded representations of basic classical simple complex Lie superalgebras; 5 The classical simple real Lie superalgebras; 6 The conformal, de Sitter and anti-de Sitter superalgebras; Part E: Infinite-Dimensional Lie Algebras and Superalgebras and their Applications; Chapter 26. The Structure of Kac-Moody Algebras; 1 Introduction to infinite-dimensional Lie algebras; 2 Construction of Kac-Moody algebras; 3 Properties of general Kac-Moody algebras; 4 Types of complex Kac-Moody algebras; 5 Affine Kac-Moody algebras; 6 Kac-Moody superalgebras.
Chapter 27. Representations of Kac-Moody Algebras1 Highest weight representations of general Kac-Moody algebras; 2 Highest weight representations of affine Kac-Moody algebras; 3 Character formulae; 4 The vertex construction of the basic representation of a simply laced untwisted affine Kac-Moody algebra; 5 Representations of untwisted affine Kac-Moody algebras in terms of fermion creation and annihilation operators; Chapter 28. The Virasoro Algebra and Superalgebras; 1 The conformal algebras; 2 Representations of the Virasoro algebra.