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

It is known that there exists a natural functor Φ 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 Ψ and Ψe that construct a Lie supergroup (thought of as a special group-valued functor) out of a given super Harish-Chandra pair, so that both Ψ and Ψe are quasi-inverse to the functor Φ.

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Lie supergroups, super Harish-Chandra pairs, Lie superalgebras
Mathematical Subject Classification
Primary: 14M30, 58A50
Secondary: 17B99
Received: 3 December 2019
Revised: 7 May 2020
Accepted: 7 May 2020
Published: 13 July 2020
Fabio Gavarini
Dipartimento di Matematica
Università degli studi di Roma “Tor Vergata”