Multiplier Hopf coquasigroup: Definition and Coactions

TL;DR

This paper introduces a new algebraic structure called multiplier Hopf coquasigroup, providing a definition, conditions for regularity, and exploring coactions and modules related to it.

Contribution

It defines multiplier Hopf coquasigroups using Galois maps and establishes criteria for their regularity, extending the theory of quantum groups.

Findings

Provided a necessary and sufficient condition for regularity.

Developed the theory of coactions and Yetter-Drinfeld modules.

Extended the framework of Hopf algebras to multiplier coquasigroups.

Abstract

This paper uses Galois maps to give a definition of generalized multiplier Hopf coquasigroups, and give a sufficient and necessary condition for a multiplier bialgebra to be a regular multiplier Hopf coquasigroup. Then coactions and Yetter-Drinfeld quasimodules of regular multiplier Hopf coquasigroups are also considered.