Abstrak

Kembali

Let Γ be a discrete group. We show that if Γ is nonamenable, then the algebraic tensor products C∗r (Γ) ⊗ C∗r (Γ) and C∗ (Γ) ⊗ C∗r (Γ) do not admit unique C∗-norms. Moreover, when Γ1 and Γ2 are discrete groups containing copies of noncommutative free groups, then C∗r (Γ1) ⊗ C∗r (Γ2) and C∗(Γ1) ⊗ C∗r (Γ2) admit 2ℵ0 C∗-norms. Analogues of these results continue to hold when these familiar group C∗-algebras are replaced by appropriate intermediate group C∗-algebras.