On functor points of affine supergroups

Akira Masuoka; Taiki Shibata

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arXiv · 1505.06558

On functor points of affine supergroups

Akira Masuoka·Taiki Shibata

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Abstract

To construct an affine supergroup from a Harish-Chandra pair, Gavarini [2] invented a natural method, which first constructs a group functor and then proves that it is representable. We give a simpler and more conceptual presentation of his construction in a generalized situation, using Hopf superalgebras over a superalgebra. As an application of the construction, given a closed super-subgroup of an algebraic supergroup, we describe the normalizer and the centralizer, using Harish-Chandra pairs. We also prove a tensor product decomposition theorem for Hopf superalgebras, and describe explicitly by cocycle deformation, the difference which results from the two choices of dualities found in literature.

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Akira Masuoka, Taiki Shibata. 2015-05-25. On functor points of affine supergroups. https://arxiv.org/abs/1505.06558

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