Matched pairs of $m$-invertible Hopf quasigroups

TL;DR

This paper extends matched pair theory from groups to a class of quasigroups called $m$-inverse property loops, introducing $m$-invertible Hopf quasigroups at the Hopf algebra level.

Contribution

It develops the theory of matched pairs for $m$-inverse property loops and introduces $m$-invertible Hopf quasigroups, expanding the algebraic framework.

Findings

Established matched pair theory for $m$-inverse property loops

Defined and studied $m$-invertible Hopf quasigroups

Extended classical theory to a new algebraic context

Abstract

The matched pair theory (of groups) is studied for a class of quasigroups; namely, the $m$-inverse property loops. The theory is upgraded to the Hopf level, and the "$m$-invertible Hopf quasigroups" are introduced.