Jones type basic construction on Hopf spin models

Let H be a finite dimensional C*-Hopf algebra and A the observable algebra of Hopf spin models. For some coaction of the Drinfeld double D(H) on A, the crossed product A ⋊ D(H) can define the field algebra F of Hopf spin models. In the paper, we study C*-basic construction for the inclusion A ⊆ F on Hopf spin models. To achieve this, we define the action α: D(H) × F → F, and then construct the resulting crossed product F ⋊ D(H), which is isomorphic A ⊗ End(D(H)). Furthermore, we prove that the C*-basic construction for A ⊆ F is consistent to F ⊗ D(H), which yields that the C*-basic constructions for the inclusion A ⊆ F is independent of the choice of the coaction of D(H) on A.