Comments about quantum symmetries of SU(3) graphs
R. Coquereaux (CPT), D. Hammaoui (LPTP), G. Schieber (LPTP, CBPF,, CPT), E.H. Tahri (LPTP)
TL;DR
This paper explores the quantum symmetries and algebraic structures of SU(3) graphs, extending ADE Dynkin diagrams, to better understand fusion properties and modular invariants in conformal field theory.
Contribution
It introduces a comprehensive set of algebraic objects and relations that describe fusion and quantum symmetries for SU(3) graphs, generalizing previous ADE classifications.
Findings
Describes algebraic structures for SU(3) quantum symmetries
Summarizes properties of individual SU(3) graph systems
Extends ADE Dynkin diagram classification to SU(3) case
Abstract
For the SU(3) system of graphs generalizing the ADE Dynkin digrams in the classification of modular invariant partition functions in CFT, we present a general collection of algebraic objects and relations that describe fusion properties and quantum symmetries associated with the corresponding Ocneanu quantum groupo\"{i}ds. We also summarize the properties of the individual members of this system.
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