Braided $\mathbb{Z}_q$-extensions of pointed fusion categories
Jingcheng Dong
TL;DR
This paper classifies specific braided extensions of pointed fusion categories and applies this to classify modular categories with a particular Frobenius-Perron dimension, advancing the understanding of their structure.
Contribution
It provides a classification of braided $bZ_q$-extensions of pointed fusion categories and modular categories of Frobenius-Perron dimension $q^3$, where $q$ is prime.
Findings
Classification of braided $bZ_q$-extensions of pointed fusion categories
Complete classification of modular categories with Frobenius-Perron dimension $q^3$
New structural insights into fusion categories related to prime dimensions
Abstract
We classify braided -extensions of pointed fusion categories, where is a prime number. As an application, we classify modular categories of Frobenius-Perron dimension .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology