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

For a finite-dimensional cocommutative semisimple Hopf C∗-algebra H and a normal coideal ∗-subalgebra H1, we define the nonbalanced quantum double DH1;H as the crossed product of H with H1op^, with respect to the left coadjoint representation of the first algebra acting on the second one, and then c...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2021, Vol.2021, p.1-8
Main Authors: Qiaoling, Xin, Tianqing, Cao
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Quantum field theory
Symmetry
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Summary:For a finite-dimensional cocommutative semisimple Hopf C∗-algebra H and a normal coideal ∗-subalgebra H1, we define the nonbalanced quantum double DH1;H as the crossed product of H with H1op^, with respect to the left coadjoint representation of the first algebra acting on the second one, and then construct the infinite crossed product AH1=⋯⋊H⋊H1^⋊H⋊H1^⋊H⋊⋯ as the observable algebra of nonbalanced Hopf spin models. Under a right comodule algebra action of DH1;H on AH1, the field algebra can be obtained as the crossed product C∗-algebra. Moreover, we prove there exists a duality between the nonbalanced quantum double DH1;H and the observable algebra AH1.
ISSN:2314-4629
2314-4785
DOI:10.1155/2021/5587878