Commutative algebras in Fibonacci categories

Thomas Booker; Alexei Davydov

doi:10.1016/j.jalgebra.2011.12.029

Commutative algebras in Fibonacci categories

Thomas Booker, Alexei Davydov

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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	https://doi.org/10.1016/j.jalgebra.2011.12.029
Publication status	Published - 2012

Keywords

Fusion category
Modular category
Vertex operator algebra

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10.1016/j.jalgebra.2011.12.029

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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.",

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AU - Davydov, Alexei

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AB - 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.

KW - Fusion category

KW - Modular category

KW - Vertex operator algebra

U2 - 10.1016/j.jalgebra.2011.12.029

DO - 10.1016/j.jalgebra.2011.12.029

M3 - Article

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VL - 355

SP - 176

EP - 204

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Commutative algebras in Fibonacci categories

Abstract

Keywords

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