The Mathematical Intelligencer

, Volume 11, Issue 1, pp 27–35 | Cite as

Why the circle is connected: An introduction to quantized topology

  • Edward G. Effros
  • A. Grothendieck
Article
First Online:

Keywords

Operator Algebra Royal Academy Trace Class Operator Positive Compact Operator Bounded Linear Transformation 
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References

  1. [1]
    B. Blackadar,K-theory for Operator Algebras, Mathematical Sciences Research Institute Publications, Vol. 5, Springer-Verlag, New York, 1986.Google Scholar
  2. [2]
    A. Connes, Non-commutative differential topology,Publ. Math. IHES 62 (1985), 257–360.CrossRefMathSciNetGoogle Scholar
  3. [3]
    J. Cuntz, K-theoretic amenability for discrete groups,J. Reine Ang. Math. 344, 180–195.Google Scholar
  4. [4]
    P. A. M. Dirac,The Derivation of Quantum Theory, Gordon and Breach, London, 1971.Google Scholar
  5. [5]
    W. Heisenberg, Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen,Zeit. für Physik 34 (1925), p. 879.CrossRefGoogle Scholar
  6. [6]
    R. Kadison and J. Ringrose,Fundamentals of the Theory of Operator Algebras, Academic Press, 1986.Google Scholar
  7. [7]
    G. Mackey,Mathematical Foundations of Quantum Mechanics, W. A. Benjamin, New York, 1963.MATHGoogle Scholar
  8. [8]
    J. von Neumann, Zur Algebra der Funktionaloperationen und Theorie der normalen Operatoren,Math. Ann. 102 (1929), 370–427.CrossRefMATHGoogle Scholar
  9. [9]
    G. Pedersen,C*-algebras and their Automorphism Groups, Academic Press, 1979.Google Scholar
  10. 10]
    M. Pimsner and D. Voiculescu, K-groups of reduced crossed products by free groups,J. Op. Theory 8 (1982), 131–156.MATHMathSciNetGoogle Scholar
  11. [11]
    R. Powers, Simplicity of the C*-algebra associated with the free group on two generators,Duke Math..49 (1975), 151–156.CrossRefMathSciNetGoogle Scholar
  12. [12]
    F. Riesz and B. Sz.-Nagy,Functional Analysis, Frederick Ungar Pub., 1955.Google Scholar
  13. [13]
    M. Takesaki,Theory of Operator Algebras, I, Springer- Verlag, 1979.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 1989

Authors and Affiliations

  • Edward G. Effros
    • 1
  • A. Grothendieck
    • 2
  1. 1.Mathematics DeptUCLALos AngelesUSA
  2. 2.Department of MathematicsUniv. Montpellier 2 PI.Eugène BataillonFrance

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