The structure of the observable algebra determined by a hopf ∗-subalgebra in hopf spin models

Let H be a finite dimensional Hopf C^∗-algebra, H₁ a Hopf ∗-subalgebra of H. This paper focuses on the observable algebra A_H1 determined by H₁ in nonequilibrium Hopf spin models, in which there is a copy of H₁ on each lattice site, and a copy of Ĥ on each link, where Ĥ denotes the dual of H. Furthermore, using the iterated twisted tensor product of finite ∗-algebras, one can prove that the observable algebra A_H1 is ∗-isomorphic to the C^∗-inductive limit · · · ⋊ H₁ ⋊ Ĥ ⋊ H₁ ⋊ Ĥ ⋊ H₁ ⋊ · · · .