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Idempotents in the reduced $ C\sp *$-algebra of a free group


Authors: Joel M. Cohen and Alessandro Figà-Talamanca
Journal: Proc. Amer. Math. Soc. 103 (1988), 779-782
MSC: Primary 46L05; Secondary 22D25
DOI: https://doi.org/10.1090/S0002-9939-1988-0947657-9
MathSciNet review: 947657
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Abstract: The purpose of this note is to give a simple proof of the theorem, originally due to M. Pimsner and D. Voiculescu, that the reduced $ {C^*}$-algebra of a free group has no nontrivial idempotents.


References [Enhancements On Off] (What's this?)

  • [CH] J. M. Cohen, $ {C^*}$-algebras without idempotents, J. Funct. Anal. 33 (1979), 211-216. MR 546507 (81a:46071)
  • [CN] A. Connes, Non commutative differential geometry, Chaps. I, II, Publ. Math. Inst. Hautes Etudes Sci. 62 (1986), 257-360. MR 823176 (87i:58162)
  • [CZ] J. Cuntz, $ K$-theoretic amenability for discrete groups, J. Reine Angew. Math. 344 (1983), 180-195. MR 716254 (86e:46064)
  • [JV] P. Julg and A. Valette, $ K$-theoretic amenability for $ {\text{S}}{{\text{L}}_2}\left( {{{\mathbf{Q}}_p}} \right)$, and the action on the associated tree, J. Funct. Anal. 58 (1984), 194-215. MR 757995 (86b:22030)
  • [K] G. Kasparov, $ K$-theory, group $ {C^*}$-algebras and higher signatures, Conspectus, Chernogolovka, 1983.
  • [L] E. C. Lance, $ K$-theory for certain group $ {C^*}$-algebras, Acta Math. 151 (1983), 209-230. MR 723010 (86f:46076)
  • [PV] M. Pimsner and D. Voiculescu, $ K$-groups of reduced crossed products by free groups, J. Operator Theory 8 (1982), 131-156. MR 670181 (84d:46092)
  • [P] R. T. Powers, Simplicity of the $ {C^*}$-algebra associated with the free group on two generators, Duke Math J. 43 (1975), 151-156. MR 0374334 (51:10534)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947657-9
Keywords: Idempotent, group algebra, free group, $ {C^*}$-algebra
Article copyright: © Copyright 1988 American Mathematical Society

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