PreprintCC BY 4.0arXiv
A Lie Correspondence in the Setting of Hopf and Frobenius Algebras
Abstract
In this paper we demonstrate that Hopf algebras and Frobenius algebras provide an appropriate setting for an analogue of the classical Lie correspondence. We introduce a compatibility structure between Hopf and Frobenius algebras called Hopf-Frobenius modules, and give constructions that can be applied to any such module, which produce corresponding Lie groups and Lie algebras. Further, we show that classical Lie algebras and Lie groups give rise to Hopf-Frobenius modules for which the corresponding Lie groups and Lie algebras produced by our construction are those of the ordinary Lie correspondence.
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BibTeX
@misc{alexander2026correspondence,
title = {{A Lie Correspondence in the Setting of Hopf and Frobenius Algebras}},
author = {Matt Alexander},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04046},
eprint = {2610.04046},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04046},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Lie Correspondence in the Setting of Hopf and Frobenius Algebras
AU - Matt Alexander
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.04046
UR - https://arxiv.org/abs/2610.04046
AB - In this paper we demonstrate that Hopf algebras and Frobenius algebras provide an appropriate setting for an analogue of the classical Lie correspondence. We introduce a compatibility structure between Hopf and Frobenius algebras called Hopf-Frobenius modules, and give constructions that can be applied to any such module, which produce corresponding Lie groups and Lie algebras. Further, we show that classical Lie algebras and Lie groups give rise to Hopf-Frobenius modules for which the corresponding Lie groups and Lie algebras produced by our construction are those of the ordinary Lie correspondence.
ER -