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 .