The Field Algebra in Hopf Spin Models Determined by a Hopf *-Subalgebra and Its Symmetric Structure

Xiaomin Wei, Lining Jiang*, Qiaoling Xin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

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 Ĥ we define the observable algebra AH1. Then using a comodule action of D(H, H1) 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, H1).

Original languageEnglish
Pages (from-to)907-924
Number of pages18
JournalActa Mathematica Scientia
Volume41
Issue number3
DOIs
Publication statusPublished - May 2021

Keywords

  • 16T05
  • 46L05
  • 46N50
  • 81R15
  • Comodule algebra
  • commutant
  • duality
  • field algebra
  • observable algebra

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Wei, X., Jiang, L., & Xin, Q. (2021). The Field Algebra in Hopf Spin Models Determined by a Hopf *-Subalgebra and Its Symmetric Structure. Acta Mathematica Scientia, 41(3), 907-924. https://doi.org/10.1007/s10473-021-0317-8