The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants

Abstract

We determine the Nakayama automorphism of the almost Calabi-Yau algebra A associated to the braided subfactors or nimrep graphs associated to each SU(3) modular invariant. We use this to determine a resolution of A as an A-A bimodule, which will yield a projective resolution of A.

46 pages which constitutes the published version, plus an Appendix detailing some long calculations. arXiv admin note: text overlap with arXiv:1110.4547

References in corpus (3)

• Calabi-Yau algebras
• A categorical and diagrammatical approach to Temperley-Lieb algebras
• The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants

Cited by in corpus (11)

• The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra
• The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants
• The category of extensions and a characterisation of $n$-exangulated functors
• Higher preprojective algebras, Koszul algebras, and superpotentials
• The Nakayama automorphism of a self-injective preprojective algebra
• Braided Subfactors, Spectral Measures, Planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants
• $K$-theory of AF-algebras from braided C*-tensor categories
• Realizing the braided Temperley-Lieb-Jones C*-tensor categories as Hilbert C*-modules
• 3-Preprojective Algebras of Type D
• Classification of Module Categories for $SO(3{)}_{2m}$
• On the homology of almost Calabi-Yau algebras associated to SU(3) modular invariants