Multiplier Hopf coquasigroups with faithful integrals

2020/08/21 by Yang, Tao
#16T05 #16T99 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2008.09525

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 \widehatA is a Hopf quasigroup, and the biduality \widehat\widehatA is isomorphic to the original A as multiplier Hopf coquasigroups. This biduality theorem also holds for a class of Hopf quasigroups with faithful integrals.

Related

• Integral Dual of some infinite dimensional Hopf quasigroups
• Multiplier Hopf coquasigroup: Definition and Coactions
• Integral theory for Hopf (co)quasigroups
• Hopf modules and the fundamental theorem for Hopf (co)quasigroups
• The cointegral theory of weak multiplier Hopf algebras