Real forms of complex Lie superalgebras and supergroups
Rings and Algebras
2023-03-21 v4 Algebraic Geometry
Representation Theory
Abstract
We investigate the notion of real form of complex Lie superalgebras and supergroups, both in the standard and graded version. Our functorial approach allows most naturally to go from the superalgebra to the supergroup and retrieve the real forms as fixed points, as in the ordinary setting. We also introduce a more general notion of compact real form for Lie superalgebras and supergroups, and we prove some existence results for Lie superalgebras that are simple contragredient and their associated connected simply connected supergroups.
Cite
@article{arxiv.2003.10535,
title = {Real forms of complex Lie superalgebras and supergroups},
author = {Rita Fioresi and Fabio Gavarini},
journal= {arXiv preprint arXiv:2003.10535},
year = {2023}
}
Comments
27 pages - This the final, published version