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

Cohen, Joel M.; Figà-Talamanca, Alessandro

doi:10.1090/S0002-9939-1988-0947657-9

Idempotents in the reduced $C^ *$-algebra of a free group
HTML articles powered by AMS MathViewer

by Joel M. Cohen and Alessandro Figà-Talamanca PDF

Proc. Amer. Math. Soc. 103 (1988), 779-782 Request permission

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

Joel M. Cohen, $C^{\ast }$-algebras without idempotents, J. Functional Analysis 33 (1979), no. 2, 211–216. MR 546507, DOI 10.1016/0022-1236(79)90112-5
Alain Connes, Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1985), 257–360. MR 823176
Joachim Cuntz, $K$-theoretic amenability for discrete groups, J. Reine Angew. Math. 344 (1983), 180–195. MR 716254, DOI 10.1515/crll.1983.344.180
Pierre Julg and Alain Valette, $K$-theoretic amenability for $\textrm {SL}_{2}(\textbf {Q}_{p})$, and the action on the associated tree, J. Funct. Anal. 58 (1984), no. 2, 194–215. MR 757995, DOI 10.1016/0022-1236(84)90039-9

-theory, group

-algebras and higher signatures

E. Christopher Lance, $K$-theory for certain group $C^{\ast }$-algebras, Acta Math. 151 (1983), no. 3-4, 209–230. MR 723010, DOI 10.1007/BF02393207
M. Pimsner and D. Voiculescu, $K$-groups of reduced crossed products by free groups, J. Operator Theory 8 (1982), no. 1, 131–156. MR 670181
Robert T. Powers, Simplicity of the $C^{\ast }$-algebra associated with the free group on two generators, Duke Math. J. 42 (1975), 151–156. MR 374334