We pursue a classification of low-rank super-modular categories parallel to that of modular categories. We classify all super-modular categories up to rank = 6, and spin modular categories up to rank = 11. In particular, we show that, up to fusion rules, there is exactly one non-split super-modular category of rank 2, 4 and 6, namely PSU(2)_4k+ 2 for k = 0,1 and 2. This classification is facilitated by adapting and extending well-known constraints from modular categories to super-modular categories, such as Verlinde and Frobenius-Schur indicator formulae.

中文翻译：

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按等级对超模块化类别进行分类

我们追求与模块化类别平行的低等级超模块化类别的分类。我们将所有超模块化类别归类为等级= 6，并将自旋模块化类别归类为等级=11。特别是，我们证明，根据融合规则，仅存在一个非拆分超模块化类别，即等级2，图4和6，即P小号ù（2）_{4 ķ + 2}为ķ = 0,1和2。这种分类是通过调整和延伸从模块化类别众所周知的约束来超模块化类别，如韦尔兰德和弗罗贝纽斯促进-Schur指标公式。