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We prove that a coaction of a Hopf algebra on another preserving the latter's associative-algebra structure and comultiplication automatically also preserves the counit, antipode, and tensor-interchange map and in fact factors through the coaction dual to an action of an affine group scheme by Hopf-algebra automorphism...
The unitary group of a von Neumann algebra on an $\aleph_0$-dimensional Hilbert space is polynomially weak$^*$-dense (equivalently, $G_{delta}$ dense or residual) in the normal unit ball if and only if the canonical finite atomic quotient of the von Neumann algebra is trivial. The analogous result holds for the usual w...
We prove that for every ergodic transformation $T$ on an infinite standard probability space both the automorphism group (i.e. centralizer) $\mathrm{Aut}(T)$ and its reversing automorphism group are realizable as symmetry groups of graphings. This is an analogue of Sabidussi's realization of arbitrary graph-automorphis...
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