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We present two novel proofs of the known classification of connected affinealgebraic supergroups $G$ such that $\operatorname{Rep}G$ is semisimple. Theproofs are geometrically motivated, although both rely on an algebraic lemmathat characterizes $\mathfrak{osp}(1|2n)$ amongst simple Lie superalgebras.

Two geometric proofs of the classification of algebraic supergroups with semisimple representation theory