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Continuous unitary projective representations of Polish groups: The BMS-group

  • U. Cattaneo
Mathematical Physics
Part of the Lecture Notes in Physics book series (LNP, volume 50)

Abstract

It is shown that every continuous unitary projective representation of a Polish group can be lifted to a Borel multiplier representation (i.e., to a representation “up to a Borel factor”) and that this, in turn, can be derived from a continuous (ordinary) representation of a Polish group obtained from a central topological extension of the group considered by the multiplicative group of all complex numbers of absolute value 1. One determines the factors of all Borel multiplier representations of the Bondi-Metzner-Sacks group when the subgroup of “supertranslations” is the additive group of a separable real Hilbert space.

Keywords

Polish Group Additive Group Neutral Element Projective Representation Superselection Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    G.W. MACKEY, Acta Math. 99, 265 (1958).Google Scholar
  2. [2]
    L. AUSLANDER and C.C. MOORE, Mem.Am.Math.Soc. No. 62 (1966).Google Scholar
  3. [3]
    P.J. McCARTHY, “Projective Representations of the Asymptotic Symmetry Group of General Relativity” in Proceedings of the 2nd International Colloquium on Group Theoretical Methods in Physics, Nijmegen, June 25–29, 1973.Google Scholar
  4. [4]
    U. CATTANEO, “On Unitary/Antiunitary Projective Representations of Groups”. To appear in Rep.Math.Phys.Google Scholar
  5. [5]
    E. WIGNER, Ann.Math. 40, 149 (1939).MathSciNetGoogle Scholar
  6. [6]
    V. BARGMANN, Ann.Math. 59, 1 (1954).Google Scholar
  7. [7]
    J. DIXMIER, Trans.Am.Math.Soc. 104, 278 (1962).Google Scholar
  8. [8]
    S. MACLANE, Homology. Springer-Verlag:Heidelberg, 1963.Google Scholar
  9. [9]
    U.CATTANEO, “Multipliers of BUM-reps of the Bondi-Metzner-Sacks group”. To appear.Google Scholar
  10. [10]
    E. HEWITT and K.A. ROSS, Abstract Harmonic Analysis I. Springer-Verlag: Heidelberg, 1963.Google Scholar
  11. [11]
    K.R. PARTHASARATHY and K. SCHMIDT, Positive Definite Kernels, Continuous Tensor Products and Central Limit Theorems of Probability Theory, Lecture Notes in Mathematics 272. Springer-Verlag: Heidelberg, 1972.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • U. Cattaneo
    • 1
  1. 1.Fachbereich PhysikUniversität KaiserslauternKaiserslauternGermany

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