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 Sofic and Hyperlinear Groups and Connes' Embedding Conjecture
  name:
    name part: Capraro, Valerio.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Lupini, Martino.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2015
    edition: 1st ed. 2015.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 151 p. online resource.
  abstract: This monograph presents some cornerstone results in the study of sofic and hyperlinear groups and the closely related Connes' embedding conjecture. These notions, as well as the proofs of many results, are presented in the framework of model theory for metric structures. This point of view, rarely explicitly adopted in the literature, clarifies the ideas therein, and provides additional tools to attack open problems. Sofic and hyperlinear groups are countable discrete groups that can be suitably approximated by finite symmetric groups and groups of unitary matrices. These deep and fruitful notions, introduced by Gromov and Radulescu, respectively, in the late 1990s, stimulated an impressive amount of research in the last 15 years, touching several seemingly distant areas of mathematics including geometric group theory, operator algebras, dynamical systems, graph theory, and quantum information theory. Several long-standing conjectures, still open for arbitrary groups, are now settled for sofic or hyperlinear groups. The presentation is self-contained and accessible to anyone with a graduate-level mathematical background. In particular, no specific knowledge of logic or model theory is required. The monograph also contains many exercises, to help familiarize the reader with the topics present.
  table of contents: Introduction -- Sofic and hyperlinear groups -- Connes' embedding conjecture -- Conclusions.
  note: by Valerio Capraro, Martino Lupini.
  subject:
    topic: Mathematics
  subject:
    topic: Group theory
  subject:
    topic: Operator theory
  subject:
    topic: Mathematics
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: Operator Theory
  classification: QA174-183
  classification: 512.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 2136
  identifier: 9783319193335
  identifier: http://dx.doi.org/10.1007/978-3-319-19333-5
  record info:
    record creation date: 151012
    record change date: 20151012161115.0
    record identifier: 978-3-319-19333-5