On the homology of almost Calabi–Yau algebras associated to SU(3) modular invariants

We compute the Hochschild homology and cohomology, and cyclic homology, of almost Calabi–Yau algebras for SU(3) ADE graphs. These almost Calabi–Yau algebras are a higher rank analogue of the preprojective algebras for Dynkin diagrams, which are SU(2)-related constructions. The Hochschild (co)homology and cyclic homology of A can be regarded as invariants for the braided subfactors associated to the SU(3) modular invariants.