Classification of Pointed Fusion Categories of dimension $p^3$ up to weak Morita Equivalence (1808.05139v1)

Abstract: We give a complete classification of pointed fusion categories over $\mathbb{C}$ of global dimension $p^3$ for $p$ any odd prime. We proceed to classify the equivalence classes of pointed fusion categories of dimension $p^3$ and we determine which of these equivalence classes have equivalent categories of modules.