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 Gred. We list some of its properties and determine Gred in the case GL(m|1).
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I would like to thank the referee for providing many useful comments on an earlier version of this paper.
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Presented by: Peter Littelmann
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Heidersdorf, T. On Supergroups and their Semisimplified Representation Categories. Algebr Represent Theor 22, 937–959 (2019). https://doi.org/10.1007/s10468-018-9806-4
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DOI: https://doi.org/10.1007/s10468-018-9806-4
Keywords
- Super tannakian category
- Semisimple category
- Negligible morphisms
- General linear supergroup
- Supergroup
- Tensor products