#### Vol. 306, No. 2, 2020

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A new equivalence between super Harish-Chandra pairs and Lie supergroups

### Fabio Gavarini

Vol. 306 (2020), No. 2, 451–485
##### 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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##### Keywords
Lie supergroups, super Harish-Chandra pairs, Lie superalgebras
##### Mathematical Subject Classification
Primary: 14M30, 58A50
Secondary: 17B99
##### Milestones
Revised: 7 May 2020
Accepted: 7 May 2020
Published: 13 July 2020
##### Authors
 Fabio Gavarini Dipartimento di Matematica Università degli studi di Roma “Tor Vergata” Roma Italy