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: Quantum Isometry Groups
  name:
    name part: Goswami, Debashish.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Bhowmick, Jyotishman.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: ii
    date issued: 2016
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXVIII, 235 p. online resource.
  abstract: This book offers an up-to-date overview of the recently proposed theory of quantum isometry groups. Written by the founders, it is the first book to present the research on the “quantum isometry group”, highlighting the interaction of noncommutative geometry and quantum groups, which is a noncommutative generalization of the notion of group of isometry of a classical Riemannian manifold. The motivation for this generalization is the importance of isometry groups in both mathematics and physics. The framework consists of Alain Connes’ “noncommutative geometry” and the operator-algebraic theory of “quantum groups”. The authors prove the existence of quantum isometry group for noncommutative manifolds given by spectral triples under mild conditions and discuss a number of methods for computing them. One of the most striking and profound findings is the non-existence of non-classical quantum isometry groups for arbitrary classical connected compact manifolds and, by using this, the authors explicitly describe quantum isometry groups of most of the noncommutative manifolds studied in the literature. Some physical motivations and possible applications are also discussed.
  table of contents: Chapter 1. Introduction -- Chapter 2. Preliminaries -- Chapter 3. Classical and Noncommutative Geometry -- Chapter 4. Definition and Existence of Quantum Isometry Groups -- Chapter 5. Quantum Isometry Groups of Classical and Quantum -- Chapter 6. Quantum Isometry Groups of Discrete Quantum Spaces -- Chapter 7. Nonexistence of Genuine Smooth CQG Actions on Classical Connected Manifolds -- Chapter 8. Deformation of Spectral Triples and Their Quantum Isometry Groups -- Chapter 9. More Examples and Computations -- Chapter 10. Spectral Triples and Quantum Isometry Groups on Group C*-Algebras.
  note: by Debashish Goswami, Jyotishman Bhowmick.
  subject:
    topic: Mathematics
  subject:
    topic: Functional analysis
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Differential geometry
  subject:
    topic: Mathematical physics
  subject:
    topic: Quantum physics
  subject:
    topic: Mathematics
  subject:
    topic: Global Analysis and Analysis on Manifolds
  subject:
    topic: Mathematical Physics
  subject:
    topic: Differential Geometry
  subject:
    topic: Functional Analysis
  subject:
    topic: Quantum Physics
  classification: QA614-614.97
  classification: 514.74
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Infosys Science Foundation Series
  identifier: 9788132236672
  identifier: http://dx.doi.org/10.1007/978-81-322-3667-2
  record info:
    record creation date: 170105
    record change date: 20170105162054.0
    record identifier: 978-81-322-3667-2