On supergroups and their semisimplified representation categories
classification
🧮 math.RT
keywords
mathcalrepresentationcategoryidealschemesupergroupcasecategories
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The representation category $\mathcal{A} = Rep(G,\epsilon)$ of a supergroup scheme $G$ has a largest proper tensor ideal, the ideal $\mathcal{N}$ of negligible morphisms. If we divide $\mathcal{A}$ by $\mathcal{N}$ we get the semisimple representation category of a pro-reductive supergroup scheme $G^{red}$. We list some of its properties and determine $G^{red}$ in the case $GL(m|1)$.
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