# Super-easy quantum groups: definition and examples

## TL;DR

This paper introduces the concept of super-easy quantum groups, providing a formal framework, examples including symplectic groups, and discussing classification challenges in the context of quantum symmetry groups.

## Contribution

It defines super-easy quantum groups, extends the formalism to include symplectic groups, and explores classification issues for these quantum groups.

## Key findings

- Some quantum groups without singletons are super-easy
- The formalism includes symplectic groups and their free versions
- Discussion on the classification of super-easy quantum groups

## Abstract

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, that we axiomatize here. Our formalism covers as well the symplectic group $Sp_n$ 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.