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*Boundaries of reduced free group C-algebras**

Authors:	Ozawa Narutaka

Institution:	Department of Mathematical Sciences University of Tokyo 3-8-1 Komaba Meguro Tokyo 153-8914 Japan Department of Mathematics UCLA Los Angeles CA 90095-1555 USA narutaka{at}ms.u-tokyo.ac.jp

Abstract:	We prove that the crossed product C-algebra C_r( ${Gamma}$ , ${partial}$ ${Gamma}$ ) of a freegroup ${Gamma}$ with its boundary ${partial}$ ${Gamma}$ sits naturally between the reducedgroup C-algebra C_r ${Gamma}$ and its injective envelope I(C_r ${Gamma}$ ). In otherwords, we have natural inclusion C_r ${Gamma}$ $sub$ C_r( ${Gamma}$ , ${partial}$ ${Gamma}$ ) $sub$ I(C_r ${Gamma}$ ) of C*-algebras.

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