The Quantum Symmetry in Nonbalanced Hopf Spin Models Determined by a Normal Coideal Subalgebra

Author:

Qiaoling Xin1ORCID,Tianqing Cao2ORCID

Affiliation:

1. School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China

2. School of Mathematical Sciences, Tiangong University, Tianjin 300387, China

Abstract

For a finite-dimensional cocommutative semisimple Hopf C -algebra H and a normal coideal -subalgebra H 1 , we define the nonbalanced quantum double D H 1 ; H as the crossed product of H with H 1 o p ^ , with respect to the left coadjoint representation of the first algebra acting on the second one, and then construct the infinite crossed product A H 1 = H H 1 ^ H H 1 ^ H as the observable algebra of nonbalanced Hopf spin models. Under a right comodule algebra action of D H 1 ; H on A H 1 , the field algebra can be obtained as the crossed product C -algebra. Moreover, we prove there exists a duality between the nonbalanced quantum double D H 1 ; H and the observable algebra A H 1 .

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

General Mathematics

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