### Abstract

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 language | English |
---|---|

Pages (from-to) | 176-204 |

Number of pages | 29 |

Journal | Journal of Algebra |

Volume | 355 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 |

### Keywords

- Fusion category
- Modular category
- Vertex operator algebra

## Fingerprint Dive into the research topics of 'Commutative algebras in Fibonacci categories'. Together they form a unique fingerprint.

## Cite this

Booker, T., & Davydov, A. (2012). Commutative algebras in Fibonacci categories.

*Journal of Algebra*,*355*(1), 176-204. https://doi.org/10.1016/j.jalgebra.2011.12.029