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^op^ 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.