Is this to be a cryptic description of some nicely classified kind of mathematical object? W/o a smoothness condition, I don't see it.
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If we use just the group <Q/Z, +>, then I think action would have to be q |-> e^(2πiq) for some i^2 = -1. But not sure how to do <R/Z, +>.
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Yes, I should have said continuous representation.
End of conversation
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