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.
(E1) imposes that the fusion multiplicities N c ab are associative, i.e., X e∈Irr(A) N e abN d ec = X f ∈Irr(A) N d af N f bc
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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.