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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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5587878 |
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| author | Xin Qiaoling Cao Tianqing |
| author_facet | Xin Qiaoling Cao Tianqing |
| author_sort | Xin Qiaoling |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f21ec0c7274e44c7af9f03d7614793d3 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f21ec0c7274e44c7af9f03d7614793d32025-02-03T06:47:03ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55878785587878The Quantum Symmetry in Nonbalanced Hopf Spin Models Determined by a Normal Coideal SubalgebraXin Qiaoling0Cao Tianqing1School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, ChinaSchool of Mathematical Sciences, Tiangong University, Tianjin 300387, ChinaFor 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.http://dx.doi.org/10.1155/2021/5587878 |
| spellingShingle | Xin Qiaoling Cao Tianqing The Quantum Symmetry in Nonbalanced Hopf Spin Models Determined by a Normal Coideal Subalgebra Journal of Mathematics |
| title | The Quantum Symmetry in Nonbalanced Hopf Spin Models Determined by a Normal Coideal Subalgebra |
| title_full | The Quantum Symmetry in Nonbalanced Hopf Spin Models Determined by a Normal Coideal Subalgebra |
| title_fullStr | The Quantum Symmetry in Nonbalanced Hopf Spin Models Determined by a Normal Coideal Subalgebra |
| title_full_unstemmed | The Quantum Symmetry in Nonbalanced Hopf Spin Models Determined by a Normal Coideal Subalgebra |
| title_short | The Quantum Symmetry in Nonbalanced Hopf Spin Models Determined by a Normal Coideal Subalgebra |
| title_sort | quantum symmetry in nonbalanced hopf spin models determined by a normal coideal subalgebra |
| url | http://dx.doi.org/10.1155/2021/5587878 |
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