  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.
