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: Topics in Noncommutative Algebra
    sub title: The Theorem of Campbell, Baker, Hausdorff and Dynkin
  name:
    name part: Bonfiglioli, Andrea.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Fulci, Roberta.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2012
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXII, 539 p. 5 illus. online resource.
  abstract: Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, Numerical Analysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: 1) fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra or not) to understand and apply the statements and numerous corollaries of the main result; 2) provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view and notation; 3) provide a thorough historical background of the results, together with unknown facts about the effective early contributions by Schur, Poincaré, Pascal, Campbell, Baker, Hausdorff and Dynkin; 4) give an outlook on the applications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type); 5) quickly enable the reader, through a description of the state-of-art and open problems, to understand the modern literature concerning a theorem which, though having its roots in the beginning of the 20th century, has not ceased to provide new problems and applications. The book assumes some undergraduate-level knowledge of algebra and analysis, but apart from that is self-contained. Part II of the monograph is devoted to the proofs of the algebraic background. The monograph may therefore provide a tool for beginners in Algebra.
  table of contents: 1 Historical Overview -- Part I Algebraic Proofs of the CBHD Theorem -- 2 Background Algebra -- 3 The Main Proof of the CBHD Theorem -- 4 Some ‘Short’ Proofs of the CBHD Theorem -- 5 Convergence and Associativity for the CBHD Theorem -- 6 CBHD, PBW and the Free Lie Algebras -- Part II Proofs of the Algebraic Prerequisites -- 7 Proofs of the Algebraic Prerequisites -- 8 Construction of Free Lie Algebras -- 9 Formal Power Series in One Indeterminate -- 10 Symmetric Algebra.
  note: by Andrea Bonfiglioli, Roberta Fulci.
  subject:
    topic: Mathematics
  subject:
    topic: Nonassociative rings
  subject:
    topic: Rings (Algebra)
  subject:
    topic: Topological groups
  subject:
    topic: Lie groups
  subject:
    topic: Differential geometry
  subject:
    topic: History
  subject:
    topic: Mathematics
  subject:
    topic: Topological Groups, Lie Groups
  subject:
    topic: History of Mathematical Sciences
  subject:
    topic: Non-associative Rings and Algebras
  subject:
    topic: Differential Geometry
  classification: QA252.3
  classification: QA387
  classification: 512.55
  classification: 512.482
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematics, 2034
  identifier: 9783642225970
  identifier: http://dx.doi.org/10.1007/978-3-642-22597-0
  record info:
    record creation date: 111010
    record change date: 20151204171945.0
    record identifier: 978-3-642-22597-0