Introduction to W*-Categories

Conference paper

Abstract

A W*-category is the natural generalization of a von Neumann algebra where, instead of taking the bounded linear mappings of a fixed Hilbert space as a model, we take the bounded linear mappings between a collection of Hilbert spaces.

Together with the elementary theory of W*-categories we present a list of examples which motivates and illustrates the general notion developed in this lecture.

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References

  1. [1]
    S. Doplicher, R. Haag, J.E. Roberts, Local Observables and Particle Statistics, Commun.Math.Phys., 23 (1971) 199–230CrossRefMATHADSMathSciNetGoogle Scholar
  2. S. Doplicher, R. Haag, J.E. Roberts, Local Observables and Particle Statistics, Commun.Math.Phys., 35 (1974) 49–85.CrossRefADSMathSciNetGoogle Scholar
  3. [2]
    S. Doplicher, R. Haag, J.E. Roberts, Fields, Observables and Gauge Transformations I, Commun.Math.Phys., 13 (1969) 1–23CrossRefMATHADSMathSciNetGoogle Scholar
  4. S. Doplicher, R. Haag, J.E. Roberts, Fields, Observables and Gauge Transformations I, Commun.Math.Phys., 15 (1969) 173–200.CrossRefMATHADSMathSciNetGoogle Scholar
  5. [3]
    S. Doplicher, J.E. Roberts, Fields, Statistics and Non- Abelian Gauge Group, Commun.Math.Phys., 28 (1972), 331–348.CrossRefADSMathSciNetGoogle Scholar
  6. [4]
    J.E. Roberts, Cross Products of von Neumann Algebras by Group Duals, Symposia Math. XX (1976).Google Scholar
  7. [5]
    M. Rieffei, Morita Equivalence for C*-Algebras and W*- Algebras, Journal of Pure and Applied Algebra, 5 (1974), p. 51–96.CrossRefMathSciNetGoogle Scholar
  8. [6]
    A. Connes, M. Takesaki, The Flow of Weights on Factors of Type III, Tohoku Math. Journal, Vol. 29, no. 4 (1977).MathSciNetGoogle Scholar
  9. [7]
    A. Connes, Sur la Theorie non Commutative de 1’Integration, Lecture Notes in Mathematics 725, Springer, Berlin-Heidelberg-New York 1979.Google Scholar
  10. [8]
    J.E. Roberts, Local Cohomology and its Structural Implica- tions for Field Theory, R.C.P. no. 25, Strasbourg, Novembre 1976.Google Scholar
  11. [9]
    W.L. Paschke, Inner Product Modules over B*-Algebras, Transactions of the American Mathematical Society, vol. 182, (1973), p. 443.Google Scholar
  12. [10]
    S. Sakai, C*-Algebras and W*-Algebras, Springer, Berlin-Heidelberg-New York 1971.Google Scholar

Copyright information

© Springer-Verlag/Wien 1980

Authors and Affiliations

  • R. Lima
    • 1
  1. 1.Centre de Physique ThéoriqueCNRSMarseilleFrance

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