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- W4212936714 abstract "Given a quasi-reductive algebraic supergroup G, we use the theory of semisimplifications of symmetric monoidal categories to define a symmetric monoidal functorΦx:Rep(G)→Rep(OSp(1|2)) associated to any given element x∈Lie(G)1¯. For nilpotent elements x, we show that the functor Φx can be defined using the Deligne filtration associated to x. We use this approach to prove an analogue of the Jacobson-Morozov Lemma for algebraic supergroups. Namely, we give a necessary and sufficient condition on odd nilpotent elements x∈Lie(G)1¯ which define an embedding of supergroups OSp(1|2)→G so that x lies in the image of the corresponding Lie algebra homomorphism." @default.
- W4212936714 created "2022-02-24" @default.
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- W4212936714 date "2022-03-01" @default.
- W4212936714 modified "2023-09-27" @default.
- W4212936714 title "Jacobson-Morozov Lemma for algebraic supergroups" @default.
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- W4212936714 doi "https://doi.org/10.1016/j.aim.2022.108240" @default.
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