[math] \newcommand{\mathds}{\mathbb}[/math]

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Prove that the easy quantum groups

[[math]] H_N\subset G\subset H_N^+ [[/math]]

must fall into one of the following two classes:

[[math]] H_N\subset G\subset H_N^{[\infty]} [[/math]]

[[math]] H_N^{[\infty]}\subset G\subset H_N^+ [[/math]]