Anomaly-free fusion category symmetries have a canonical trivial phase, and the three Rep†(D8) symmetry-protected topological phases are explicitly realized by Q-system lattice models connected by an S3 duality.
Finite Quantum Groupoids and Their Applications
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We give a survey of the theory of finite quantum groupoids (weak Hopf algebras), including foundations of the theory and applications to finite depth subfactors, dynamical deformations of quantum groups, and invariants of knots and 3-manifolds.
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Non-invertible SPTs: an on-site realization of (1+1)d anomaly-free fusion category symmetry
Anomaly-free fusion category symmetries have a canonical trivial phase, and the three Rep†(D8) symmetry-protected topological phases are explicitly realized by Q-system lattice models connected by an S3 duality.