Multiplier Hopf coquasigroups with faithful integrals

Abstract

Let $A$ be a multiplier Hopf coquasigroup. If the faithful integrals exist, then they are unique up to scalar. Furthermore, if $A$ is of discrete type, then its integral duality $\hat{A}$ is a Hopf quasigroup, and the biduality $\hat{\hat{A}}$ is isomorphic to the original $A$ as multiplier Hopf coquasigroups. This biduality theorem also holds for a class of Hopf quasigroups with faithful integrals.

17 pages. arXiv admin note: substantial text overlap with arXiv:2008.07199

References in corpus (2)

• Integral theory for Hopf (co)quasigroups
• Integral Dual of some infinite dimensional Hopf quasigroups