Abstract

The structure of the observable algebra determined by a Hopf * -subalgebra in Hopf spin models

Xiaomin Wei, Lining Jiang, Qiaoling Xin

Let H be a finite dimensional Hopf C*-algebra, H1 a Hopf ∗-subalgebra of H. This paper focuses on the observable algebraAH1 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 algebraAH1 is ∗-isomorphic to the C*-inductive limit · · · oH1 o Ĥ oH1 o Ĥ oH1 o · · ·