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Unitary representations and von Neumann's continuous geometries
Friedrich Martin Schneider, Andreas Thom
We prove that the unit group of a non-discrete irreducible, continuous ring, in the sense of John von Neumann, does not admit any non-trivial unitary representation continuous with…
Projective simplicity and Bergman's property for unit groups of continuous rings
Friedrich Martin Schneider
We prove that the projective unit group , i.e., the quotient of the unit group modulo its center, of any non-discrete irreducible, continuous ring…
Geometric properties of unit groups of von Neumann's continuous rings
Friedrich Martin Schneider
We prove that, if is a non-discrete irreducible, continuous ring, then its unit group , equipped with the topology generated by the rank metric, is topologicall…
Width bounds and Steinhaus property for unit groups of continuous rings
Josefin Bernard, Friedrich Martin Schneider
We prove an algebraic decomposition theorem for the unit group of an arbitrary non-discrete irreducible, continuous ring (in von Neumann's sense), which entail…