On the classification of non-self-dual modular categories

TL;DR

This paper introduces a symbolic computational method to classify low-rank non-self-dual modular categories, specifically focusing on pseudo-unitary cases of rank up to 5, expanding understanding of their structure.

Contribution

The paper presents a novel computational approach for classifying non-self-dual modular categories of low rank, filling a gap in the existing classification literature.

Findings

Classified all pseudo-unitary non-self-dual modular categories of rank ≤ 5.

Developed a symbolic computational technique applicable to low-rank modular categories.

Identified structural properties unique to non-self-dual cases.

Abstract

We develop a symbolic computational approach to classifying low-rank modular categories. We use this technique to classify pseudo-unitary 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.