Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Alexander, Matt
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220677047