On supergroups and their semisimplified representation categories
Thorsten Heidersdorf

TL;DR
This paper studies the structure of supergroup representation categories, identifies the largest tensor ideal, and describes the resulting semisimple category, including an explicit case for $GL(m|1)$.
Contribution
It characterizes the semisimplification of supergroup representation categories and explicitly determines the reductive supergroup for $GL(m|1)$.
Findings
Identification of the largest proper tensor ideal in supergroup categories
Description of the semisimple quotient category and its properties
Explicit determination of the reductive supergroup for $GL(m|1)$
Abstract
The representation category of a supergroup scheme has a largest proper tensor ideal, the ideal of negligible morphisms. If we divide by we get the semisimple representation category of a pro-reductive supergroup scheme . We list some of its properties and determine in the case .
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