Jones type C-basic construction in non-equilibrium Hopf spin models

Let H be a finite dimensional Hopf C*-algebra, and let K be a Hopf *-subalgebra of H . Considering that the field algebra ℱ K of a non-equilibrium Hopf spin model carries a D ( H, K )-invariant subalgebra A K , this paper shows that the C*-basic construction for the inclusion A K ⊆ ℱ K can be expressed as the crossed product C*-algebra ℱ K ⋊ D ( H , K ) . Here, D ( H, K ) is a bicrossed product of the opposite dual H o p ^ and K . Furthermore, the natural action of D ( H , K ) ^ on D ( H, K ) gives rise to the iterated crossed product ℱ K ⋊ D ( H , K ) ⋊ D ( H , K ) ^ , which coincides with the C*-basic construction for the inclusion ℱ K ⊆ ℱ K ⋊ D ( H , K ) . In the end, the Jones type tower of field algebra ℱ K is obtained, and the new field algebra emerges exactly as the iterated crossed product.