Screen LibraryIntroduction to finite and infinite dimensional lie (super)algebras /
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| Main Authors: | |
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| Published: |
Academic Press, an imprint of Elsevier,
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| Publisher Address: | Amsterdam : |
| Publication Dates: | [2016] |
| Literature type: | Book |
| Language: | English |
| Subjects: | |
| Carrier Form: | xxii, 489 pages : illustrations ; 24 cm |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: |
9780128046753 (hardback) : 0128046759 |
| Index Number: | QA252 |
| CLC: | O152.5 |
| Call Number: | O152.5/S853 |
| Contents: |
Front Cover; Introduction to Finite and Infinite Dimensional Lie (Super) algebras; Copyright; Dedication; Contents; About the author; Acknowledgement; Preface; Author Acknowledgements; Chapter 1: Finite-dimensional Lie algebras; 1.1 Basic definition of Lie algebras with examples and structure constants; A Lie algebra can also be defined starting from the definition of an algebra; Lie algebras of one, two, and three dimensions and their structure constants; 1.2 Subalgebras of Lie algebras and different classes of subalgebras of gl(n, C); 1.2.1 Different subalgebras of gl(n, C). Four families of classical Lie algebras, namely, An, Bn, Cn, and Dn and their bases1.3 Ideals, quotient Lie algebras, derived sub Lie algebras, and direct sum; 1.4 Simple Lie algebras, semisimple Lie algebras, solvable and nilpotent Lie algebras; 1.5 Isomorphism theorems, Killing form, and some basic theorems; Examples for the matrix of the Killing form; 1.6 Derivation of Lie algebras; 1.7 Representations of Lie algebras and representations of sl(2,C); Representation of sl(2,C) in an (n + 1)-dimensional vector space. General theory of the representation of sl(2,C). Throughout this section G denotes sl(2,C)1.8 Rootspace decomposition of semisimple Lie algebras; Basic properties of root systems; Root space decomposition and properties of Killing form; 1.9 Root system in Euclidean spaces and root diagrams; 1.10 Coxeter graphs and Dynkin diagrams; 1.11 Cartan matrices, ranks, and dimensions of simple Lie algebras; Cartan matrices of classical simple Lie algebras; 1.12 Weyl groups and structure of Weyl groups of simple Lie algebras. 1.13 Root systems of classical simple Lie algebras and highest long and short roots1.14 Universal enveloping algebras of Lie algebras; The above definition can also be written as follows; The universal mapping property; 1.15 Representation theory of semisimple Lie algebras; 1.16 Construction of semisimple Lie algebras by generators and relations; 1.17 Cartan-Weyl basis; 1.18 Character of a finite-dimensional representation and Weyl dimension formula; 1.19 Lie algebras of vector fields; Some basic properties of Lie algebras of vector fields; Exercises; Chapter 2: Kac-Moody algebras. 2.1 Basic concepts in Kac-Moody algebrasHence for a symmetrizable Cartan matrix, one can give the following definition for Kac-Moody algebra; 2.2 Classification of finite, affine, hyperbolic, and extended-hyperbolic Kac-Moody algebras and their Dynkin diagrams; Properties of Dynkin diagrams; Dynkin diagrams for affine types; Properties of matrices of finite and affine types; For a GCM of affine type, Dynkin diagrams of A and At; Some properties of Dynkin diagrams of hyperbolic types; Some examples of Cartan matrices of hyperbolic types and their Dynkin diagrams. |