Central Extensions and Physics

1987
52 pages
Published in:
  • J.Geom.Phys. 4 (1987) 207-258

Citations per year

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Abstract: (Elsevier)
In this paper two themes are considered; first of all we consider the question under what circumstances a central extension of the Lie algebra of a given Lie group determines a central extension of this Lie group (and how many different ones). The answer will be that if we give the algebra extension in the form of a left invariant closed 2-form ω on the Lie group, then there exists an associated group extension iff the group of periods of ω is a discrete subgroup of IR and ω admits a momentum mapping for the left action of the group on itself.
  • Central extensions
  • prequantization
  • 22E99
  • 58F06
  • 22E41
  • 57T10
  • ALGEBRA: LIE
  • ALGEBRA: CENTRAL CHARGE
  • GROUP THEORY
  • MATHEMATICAL METHODS: DIFFERENTIAL GEOMETRY
  • [Barr]

    De quelques aspects de la théorie des Q-variétés différentielles et analytiques

    • R. Barre
      • Annales Inst.Fourier 23 (1973) 227
  • [Bau]

    Quantum mechanics and symmetry

    • G.G.A. Bauerle
  • [Br]

    Representations of compact Lie groups

    • Brocker
      ,
    • Th.
      ,
    • T. tom Dieck
  • [Ca]

    La topologie des espaces représentatifs des groupes de Lie

    • E. Cartan
      • Oeuvres complètes I 2 (1952) 1307
  • [Ch]

    Properties of infinite dimensional hamiltonian systems

    • P.R. Chernoff
      ,
    • J.E. Marsden
  • [Di]

    The principles of quantum mechanics

    • P.A.M. Dirac
  • [Do]

    Reveˆtements et groupe fondamental des espaces différentiels homogènes

    • P. Donato
  • [Du]

    Hyperfine interaction in a classical hydrogen atom and geometric quantization

    • C. Duval
      ,
    • J. Elhadad
      ,
    • G.M. Tuynman
      • J.Geom.and Phys. 3 (1986) 401
  • [Gu]

    Symplectic techniques in physics

    • V. Guillemin
      ,
    • S. Sternberg
  • [Hi]

    Topological methods in algebraic geometry

    • F. Hirzebruch
  • [Hi]

    A course in homological algebra

    • P.J. Hilton
      ,
    • U. Stammbach
  • [Ho]

    Group extensions of Lie groups I & II

    • G. Hochschild
      • Annals Math. 54 (1951) 96
  • [Ho]

    Group extensions of Lie groups I & II

    • G. Hochschild
      • Annals Math. 54 (1951) 537
  • [Ko]

    Quantization and unitary representations

    • B. Kostant
  • [La]

    Differential manifolds

    • S. Lang
  • [Pij]

    Self-dual Yang-Mills equations

    • Ee.M. de Jager
      ,
    • H.G.J. Pijls
      ,
    • H.G.J. Pijls
  • [Sh]

    Group extensions of compact Lie groups

    • A. Shapiro
      • Annals Math. 50 (1949) 581
  • [Si,1]

    Lie groups and quantum mechanics

    • D.J. Simms
  • [Si,2]

    Projective representations, symplectic manifolds and extensions of Lie algebras

    • D.J. Simms
  • [Si]

    Lectures on geometric quantization

    • D.J. Simms
      ,
    • N. Woodhouse
  • [Sn]

    Geometric quantization and quantum mechanics

    • J. Sniatycki
  • [So,1]

    Structures des systémes dynamiques

    • J.M. Souriau