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

2011/11/15 by Evans, David E., Pugh, Mathew
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1111.3585

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.

Related

• Hochschild homology and cohomology of down-up algebras
• Pre-Calabi-Yau algebras and oriented gravity properad
• Hochschild and cyclic homology of Yang-Mills algebras
• Hochschild (co)homology for odd Khovanov arc algebras
• Calabi-Yau algebras