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We show that each M± is isomorphic to an amalgamated free product of type I von Neumann algebras with amalgamation over a fixed discrete type I von Neumann subalgebra.
Sebastien Vasey, Saturation and solvability in abstract elementary classes with amalgamation, Archive for Mathematical Logic 56 (2017), nos.
Monica VanDieren and Sebastien Vasey, Symmetry in abstract elementary classes with amalgamation, Archive for Mathematical Logic 56 (2017), no. 3, 423 452.
We prove that the R-cyclicity of A1, …, As is equivalent to a property of C namely that C is free from Md(C), with amalgamation over D.
In particular, it is shown to include group C⁎-algebras, both reduced and full, of certain amalgamated free products of amenable groups, as well as all free products of nuclear C⁎-algebras with amalgamation over a common nuclear C⁎-subalgebra.
We give new characterizations to ensure that a free product of groups with amalgamation has a simple reduced group C⁎-algebra, and provide a concrete example of an amalgam with trivial kernel, such that its reduced group C⁎-algebra has a unique tracial state, but is not simple.
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