THE FIELD ALGEBRA IN HOPF SPIN MODELS DETERMINED BY A HOPF -SUBALGEBRA AND ITS SYMMETRIC STRUCTURE

• Published in: 数学物理学报（英文版） 2021, Vol.41 (3), p.907-924
• Main Authors: Xiaomin WEI, Lining JIANG, Qiaoling XIN
• Format: Article
• Language: English
• ISSN: 0252-9602
• DOI: 10.3969/j.issn.0252-9602.2021.03.017

Denote a finite dimensional Hopf C*-algebra by H,and a Hopf *-subalgebra of H by H1.In this paper,we study the construction of the field algebra in Hopf spin models determined by H1 together with its symmetry.More precisely,we consider the quantum double D(H,H1)as the bicrossed product of the opposite dual Hop of H and H1 with respect to the coadjoint representation,the latter acting on the former and vice versa,and under the non-trivial commutation relations between H1 and H we define the observable algebra AH1·Then using a comodule action of D(H,Hi)on AH1,we obtain the field algebra FH1,which is the crossed product AH1(×)D(H,H1),and show that the observable algebra AH1 is exactly a D(H,H1)-invariant subalgebra of FH1.Furthermore,we prove that there exists a duality between D(H,H1)and AH1,implemented by a *-homomorphism of D(H,H 1).