rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Introduction to finite and infinite dimensional lie (super)algebras
  name:
    name part: Sthanumoorthy, N. (Neelacanta)
    name part: 1945-
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: ScienceDirect (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: ne
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource
  abstract: Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras.
  table of 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).
  table of contents: 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.
  table of contents: 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.
  table of contents: 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.
  table of contents: 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.
  note: N. Sthanumoorthy.
  note: Includes bibliographical references and index.
  subject:
    topic: Lie algebras
  subject:
    topic: Algèbres de Lie
  subject:
    topic: MATHEMATICS
    topic: Algebra
    topic: Intermediate
  subject:
    topic: Lie algebras
  classification: QA252.3
  classification: 512/.55
  related item:
    title info:
      title: Introduction to Finite and Infinite Dimensional Lie (Super)algebras
    name:
      name part: Sthanumoorthy, Neelacanta.
    origin info:
      publisher: San Diego : Elsevier Science, ©2016
  identifier: 9780128046838
  identifier: 012804683X
  identifier: 9780128046753
  identifier: 0128046759
  identifier: 8874103065823753825 TotalBoox
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: N$T
    record creation date: 160429
    record change date: 20260327150425.9
    record identifier: in00005760394
    language of cataloging:
      language term: eng