Blattner–Montgomery’s Duality-Type Theorem for Hopf Coquasigroups

In this paper, we mainly prove an analogue of Blattner–Montgomery’s duality-type theorem (A⋊H)#H^≅A⊗(H#H^) in the setting of an infinite-dimensional Hopf quasigroup H with a left integral, where A⋊H is the smash product for a left H-quasimodule algebra A. In particular, let A be a left H-module algebra over an infinite dimensional coFrobenius Hopf algebra H. Then, we obtain a new result (A#H)#H^≅A⊗(H#H^) in the setting of Hopf algebras as a corollary of our main result.