Commutative algebras in Fibonacci categories

Thomas Booker, Alexei Davydov

    Research output: Contribution to journalArticle

    4 Citations (Scopus)


    By studying NIM-representations we show that the Fibonacci category and its tensor powers are completely anisotropic; that is, they do not have any non-trivial separable commutative ribbon algebras. As an application we deduce that a chiral algebra with the representation category equivalent to a product of Fibonacci categories is maximal; that is, it is not a proper subalgebra of another chiral algebra. In particular the chiral algebras of the Yang–Lee model, the WZW models of G₂ and F₄ at level 1, as well as their tensor powers, are maximal.
    Original languageEnglish
    Pages (from-to)176-204
    Number of pages29
    JournalJournal of Algebra
    Issue number1
    Publication statusPublished - 2012


    • Fusion category
    • Modular category
    • Vertex operator algebra

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