A new class of two-dimensional lattice symmetries is anomaly-free yet obstructs both gauging and on-site realization, with the obstruction classified by H^2(G,Q+).
We conclude that the equivalence class [ω] ∈ H 2(G, Q+) is a well-defined quantity insensitive to the particular choice of restriction
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Anomaly-free symmetries with obstructions to gauging and onsiteability
A new class of two-dimensional lattice symmetries is anomaly-free yet obstructs both gauging and on-site realization, with the obstruction classified by H^2(G,Q+).