Quasidiagonal Extensions of the Reduced Group C*-algebras of Certain Discrete Groups
Let G be countable group containing a free subgroup F of finite index. We show that the reduced group C *-algebra C red * (G) has a quasidiagonal extension. Our proof is based on a result of Haagerup and Thorbjørnsen [HT]_asserting the existence of such an extension of C red * (F) when F is a free group of rank greater than one. A consequence of our result is that if G is a free product of finitely many (non-trivial) cyclic groups and Γ≠Z 2*ℤ2 Z2, then Ext(C red *(Γ)) is not a group.
KeywordsQuasi diagonal extension reduced group C*-algebra free product of cyclic groups
Mathematics Subject Classification (2000)Primary 46L05 Secondary 46L45 46L35
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