Twisted Smash Products and L-R Smash Products for Biquasimodule Hopf Quasigroups

Abstract

We consider two new algebras from an H-biquasimodule algebra A and a Hopf quasigroup H: twisted smash product A ⊛ H and L-R smash product A⋇H, and find necessary and sufficient conditions for making them Hopf quasigroups. We generalize the main results in Brzeziński and Jiao [5] and Klim and Majid [9]. Moreover, if H is a cocommutative Hopf quasigroup, we prove that A ⊛ H is isomorphic to A⋇H as Hopf quasigroups.