On the classification of the Grothendieck rings of non-self-dual modular categories

We develop a symbolic computational approach to classifying low-rank modular fusion categories, up to finite ambiguity. By a generalized form of Ocneanu rigidity due to Etingof, Ostrik and Nikshych, it is enough to classify modular fusion algebras of a given rank—that is, to determine the possible Grothendieck rings with modular realizations. We use this technique to classify modular categories of rank at most 5 that are non-self-dual, i.e. those for which some object is not isomorphic to its dual object.