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arXiv · 2503.20317

Harish-Chandra pairs and affine algebraic group schemes in the Verlinde category, revisited

Akira Masuoka
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Abstract

Recently, Venkatesh extended the category equivalence between affine algebraic groups and Harish-Chandra pairs, which was proved by the author in the supersymmetric context, to the situation of the Verlinde category in positive characteristic. But the proof is incomplete at some basic point, the author thinks. Amending that we refine the result. Our construction of an affine algebraic group scheme from a Harish-Chandra pair, which uses functor points and formal group schemes, is more conceptual and simpler than the known ones of the existing literature. In the same situation we prove tensor product decomposition of commutative Hopf algebras not necessarily of finite type, which is new.

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Akira Masuoka. 2025-05-10. Harish-Chandra pairs and affine algebraic group schemes in the Verlinde category, revisited. https://arxiv.org/abs/2503.20317

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