Jones Type Basic Construction on Hopf Spin Models

Cao Tianqing, Xin Qiaoling, Wei Xiaomin and Jiang Lining
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Cao Tianqing: School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
Xin Qiaoling: School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China
Wei Xiaomin: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
Jiang Lining: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Mathematics, 2020, vol. 8, issue 9, 1-9

Abstract: Let H be a finite dimensional C ∗ -Hopf algebra and A the observable algebra of Hopf spin models. For some coaction of the Drinfeld double D ( H ) on A , the crossed product A ? D ( H ) ^ can define the field algebra F of Hopf spin models. In the paper, we study C ∗ -basic construction for the inclusion A ⊆ F on Hopf spin models. To achieve this, we define the action α : D ( H ) × F → F , and then construct the resulting crossed product F ? D ( H ) , which is isomorphic A ⊗ End ( D ( H ) ^ ) . Furthermore, we prove that the C ∗ -basic construction for A ⊆ F is consistent to F ? D ( H ) , which yields that the C ∗ -basic constructions for the inclusion A ⊆ F is independent of the choice of the coaction of D ( H ) on A .

Keywords: Hopf algebras; observable algebras; basic construction; crossed product (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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