On supergroups and their semisimplified representation categories

Abstract

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 $GL(m|1)$.

arXiv commentv3: Improved exposition, fixed minor mistakes v2: fixed typos, added some definitions