Algebraic supergroups and Harish-Chandra pairs over a commutative ring

Masuoka, Akira; Shibata, Taiki

doi:10.1090/tran/6751

Algebraic supergroups and Harish-Chandra pairs over a commutative ring
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by Akira Masuoka and Taiki Shibata PDF

Trans. Amer. Math. Soc. 369 (2017), 3443-3481 Request permission

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 reconstruct the Chevalley $\mathbb {Z}$-supergroups constructed by Fioresi and Gavarini (2012) and by Gavarini (2014). For a wide class of algebraic supergroups we describe their representations by using their super-hyperalgebras.

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