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

TL;DR

This paper calculates the Nakayama automorphism for a class of almost Calabi-Yau algebras linked to SU(3) modular invariants, providing a bimodule resolution useful for algebraic analysis.

Contribution

It explicitly determines the Nakayama automorphism for these algebras and constructs a projective bimodule resolution, advancing understanding of their structure.

Findings

Explicit Nakayama automorphism for the algebra A

Construction of a bimodule resolution of A

Enhanced understanding of algebraic structure related to SU(3) 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.