Commutative algebras in Fibonacci categories

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 pr...

Full description

Saved in:
Bibliographic Details
Published in:Journal of algebra 2012-04, Vol.355 (1), p.176-204
Main Authors: Booker, Thomas, Davydov, Alexei
Format: Article
Language:English
Subjects:
Fusion category
Modular category
Vertex operator algebra
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2011.12.029