We investigate the “two-parameter” quantum symmetry groups that we previously constructed with Skalski, with the conclusion that some of these quantum groups, namely those without singletons, are “super-easy” in a suitable sense, which we axiomatize here. Our formalism also covers the symplectic group Spn and its free version Sp+n, and some other interesting examples. Finally, we address the general problem of classifying the super-easy quantum groups, and we make a few comments on it.
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