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Abstract
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It is known that there exists a natural functor
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
and
that construct a Lie supergroup (thought of as a special group-valued
functor) out of a given super Harish-Chandra pair, so that both
and
are quasi-inverse
to the functor
.
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Keywords
Lie supergroups, super Harish-Chandra pairs, Lie
superalgebras
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Mathematical Subject Classification
Primary: 14M30, 58A50
Secondary: 17B99
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Milestones
Received: 3 December 2019
Revised: 7 May 2020
Accepted: 7 May 2020
Published: 13 July 2020
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