MPO symmetries are governed by pre-bialgebras; the anomalous Z2 symmetry of the XX model yields a non-semisimple representation category and new mixed-state fixed points.
Proposition F.1 (Vertical canonical form)
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Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries
MPO symmetries are governed by pre-bialgebras; the anomalous Z2 symmetry of the XX model yields a non-semisimple representation category and new mixed-state fixed points.