Vol. 306, No. 2, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
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 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.

Keywords
Lie supergroups, super Harish-Chandra pairs, Lie superalgebras
Mathematical Subject Classification
Primary: 14M30, 58A50
Secondary: 17B99
Milestones
Received: 3 December 2019
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