Weak Hopf Quasigroups

TL;DR

This paper introduces weak Hopf quasigroups, generalizing existing algebraic structures, and establishes their fundamental properties and theorems related to Hopf modules.

Contribution

It defines weak Hopf quasigroups and proves the fundamental theorem of Hopf modules for these structures, extending prior algebraic frameworks.

Findings

Introduction of weak Hopf quasigroups as a new algebraic structure

Proof of the fundamental theorem of Hopf modules for these structures

Main properties and characteristics of weak Hopf quasigroups

Abstract

In this paper we introduce the notion of weak Hopf quasigroup as a generalization of weak Hopf algebras and Hopf quasigroups. We obtain its main properties and we prove the fundamental theorem of Hopf modules for these algebraic structures.