Group-theoretical property of non-degenerate fusion categories of FP-dimension $p^2q^3$ and $p^3q^3$

TL;DR

This paper proves that certain non-degenerate fusion categories with specific Frobenius-Perron dimensions are group-theoretical, expanding understanding of their algebraic structure based on prime factorization conditions.

Contribution

It establishes that non-degenerate fusion categories with FP-dimensions $p^2q^3d$ and $p^3q^3d$ are group-theoretical under specified conditions, a new classification result.

Findings

Fusion categories of dimensions $p^2q^3d$ and $p^3q^3d$ are group-theoretical.

Results depend on prime factorization and square-free conditions.

Advances classification of fusion categories based on FP-dimension.

Abstract

In this paper, we show that non-degenerate fusion categories of FP-dimensions $p^2q^3d$ and $p^3q^3d$ are group-theoretical, where $p, q$ are odd primes, $d$ is a square-free integer such that $(pq,d) = 1$.