On the tensor products of simple JC-algebras (Q1337421)

In an earlier paper [Quart. J. Math. Oxford 45, 77-90 (1994)] the authoress studied the properties of the JC-tensor product \(\text{JC} (A \otimes_ \lambda B)\) of two JC-algebras \(A\) and \(B\) relative to a \(C^*\)-norm \(\lambda\) on the algebraic tensor product \(C^*(A) \otimes C^*(B)\), where \(C^*(A)\) is the universal enveloping \(C^*\)-algebra of \(A\). By studying a large number of cases, using certain quite general results, she describes the JC-tensor product \(\text{JC} (A \otimes_{\min} B)\) of two simple JC-algebras \(A\) and \(B\) relative to the minimum \(C^*\)-norm. In particular she shows that, in contrast to the result for \(C^*\)-algebras, \(\text{JC} (A \otimes_{\min} B)\) is not always simple.