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Extensions of Groups and Simple C*-Algebras

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Part of the Operator Theory: Advances and Applications book series (OT, volume 43)

Abstract

Since Powers ([9]) proved that the reduced C*-algebra of the free group on two generators C r * (F2) is simple with unique trace, several other classes consisting of discrete groups G such that C r * (G) is simple with unique trace have been produced (see e.g. [1], [4]).

Keywords

Normal Subgroup Conjugacy Class Operator Algebra Discrete Group Combinatorial Property 
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References

  1. 1.
    Akemann, C.A.; Lee, T.Y.: Some simple C*-algebra associated with free groups, Indiana Univ. Math. J. 29(1980), 505–511.CrossRefGoogle Scholar
  2. 2.
    Akemann, C.A.; Ostrand, P.: Computing norms in group C*-algebras, Amer. J. Math. 98(1976), 1015–1047.CrossRefGoogle Scholar
  3. 3.
    Boca, F.; Nit̹ică, V.: Combinatorial properties of groups and simple C*-algebras with a unique trace, J. Operator Theory 20(1988), 183–196.Google Scholar
  4. 4.
    de la Harpe, P.: Reduced C*-algebras of discrete groups which are simple with a unique trace, in Operator algebras and their connections with topology and ergodic theory, Lecture Notes in Math., vol.1132, Springer-Verlag, 1983, pp. 230–253.CrossRefGoogle Scholar
  5. 5.
    Lyndon, R.; Schupp, P.: Combinatorial group theory, Springer-Verlag, 1977.Google Scholar
  6. 6.
    Magnus, W.; Karrass, A.; Solitar, D.: Combinatorial group theory (Russian), Nauka, 1974.Google Scholar
  7. 7.
    Murray, F.; von Neumann, J.: Rings of operators. IV, Ann. of Math. 44(1943), 716–808.CrossRefGoogle Scholar
  8. 8.
    Paschke, W.; Salinas, N.: C*-algebras associated with free products of groups, Pacific J. Math. 82(1979), 211–221.Google Scholar
  9. 9.
    Powers, R.: Simplicity of the C*-algebras associated with the free group on two generators, Duke Math. J. 42(1975), 151–156.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel 1990

Authors and Affiliations

  1. 1.Department of MathematicsINCRESTBucharestRomania

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