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arXiv · 1304.0531

Algebraic supergroups and Harish-Chandra pairs over a commutative ring

Akira Masuoka·Taiki Shibata
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Abstract

We prove a category equivalence between algebraic supergroups and Harish-Chandra pairs over a commutative ring which is $2$-torsion free. The result is applied to re-construct the Chevalley $\mathbb{Z}$-supergroups constructed by Fioresi and Gavarini [8] and by Gavarini [9, 10]. For a wide class of algebraic supergroups we describe their representations by using their super-hyperalgebras.

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Akira Masuoka, Taiki Shibata. 2013-04-02. Algebraic supergroups and Harish-Chandra pairs over a commutative ring. https://arxiv.org/abs/1304.0531

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