On the fusion algebras of bimodules arising from Goodman-de la Harpe-Jones subfactors

zbMATH Open1303.46050arXiv1212.4587MaRDI QIDQ5495376

Satoshi Goto

Publication date: 4 August 2014

Abstract: By using Ocneanu's result on the classification of all irreducible connections on the Dynkin diagrams, we show that the dual principal graphs as well as the fusion rules of bimodules arising from any Goodman-de la Harpe-Jones subfactors are obtained by a purely combinatorial method. In particular we obtain the dual principal graph and the fusion rule of bimodules arising from the Goodman-de la Harpe-Jones subfactor corresponding to the Dynkin diagram $E_8$. As an application, we also show some subequivalence among $A$-$D$-$E$ paragroups.

Full work available at URL: https://arxiv.org/abs/1212.4587

zbMATH Keywords

subfactorfusion rulesDynkin diagram

Mathematics Subject Classification ID

Subfactors and their classification (46L37)

Related Items (2)

Generalized Goodman-Harpe-Jones construction of subfactors. II ⋮ \(\alpha\)-induction for bi-unitary connections

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