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

TL;DR

This paper computes Hochschild, cyclic homology, and cohomology of almost Calabi-Yau algebras linked to SU(3) ADE graphs, revealing invariants for braided subfactors related to SU(3) modular invariants.

Contribution

It extends the understanding of Calabi-Yau algebras to higher rank SU(3) cases, providing explicit homological invariants for these structures.

Findings

Computed Hochschild homology and cohomology for SU(3) algebras.

Determined cyclic homology as an invariant for braided subfactors.

Linked algebraic invariants to SU(3) modular invariants.

Abstract

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 pre-projective 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.