Abstract

It is known that there exists a natural functor $\Phi$ from Lie supergroups to super Harish-Chandra pairs. A functor going backwards, that associates a Lie supergroup with each super Harish-Chandra pair, yielding an equivalence of categories, was found by Koszul (1983), and later generalized by several authors.

We provide two new backwards equivalences, i.e., two different functors ${\Psi }^{\circ }$ and ${\Psi }^e$ that construct a Lie supergroup (thought of as a special group-valued functor) out of a given super Harish-Chandra pair, so that both ${\Psi }^{\circ }$ and ${\Psi }^e$ are quasi-inverse to the functor $\Phi$.

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