Continuum of ideals in \(R(\Phi_ 2)\otimes _{\max}R'(\Phi_ 2)\) (Q1074824)

Let \(R(\Phi_ 2)\) denote the \(W^*\)-algebra generated by the family \(\{\) U(g): \(g\in \Phi_ 2\}\) of unitary operators on the Hilbert space \(L_ 2(\Phi_ 2)\) of complex-valued functions \(\xi\) on the free group \(\Phi_ 2\) on two generators such that \(\sum_{g\in \Phi_ 2}| \xi (g)|^ 2<\infty.\) Using Connes' results on automorphisms the author shows that there exists a continuum of ideals on the projective \(C^*\)-tensor product \(R(\Phi_ 2)\otimes_{\max}R(\Phi_ 2)'\) of the type \(II_ 1\) factor \(R(\Phi_ 2)\) with its commutant \(R(\Phi_ 2)'\).