CSS* groups yield prime group von Neumann algebras, are non-inner amenable and properly proximal, and are either C*-simple with simple commutator subgroup or lack both; they are not acylindrically hyperbolic.
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On Similarity Structure Groups and their W$^*$ and C$^*$-Algebras
CSS* groups yield prime group von Neumann algebras, are non-inner amenable and properly proximal, and are either C*-simple with simple commutator subgroup or lack both; they are not acylindrically hyperbolic.