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.
Gavarini, F. (2020). A new equivalence between super Harish-Chandra pairs and Lie supergroups. PACIFIC JOURNAL OF MATHEMATICS, 306(2), 451-485 [10.2140/pjm.2020.306.451].
A new equivalence between super Harish-Chandra pairs and Lie supergroups
Gavarini, Fabio
2020-07-13
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.| File | Dimensione | Formato | |
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