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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 r e d . We list some of its properties and determine G r e d  in the case GL(m|1).

On Supergroups and their Semisimplified Representation Categories