# Prime decomposition of modular tensor categories of local modules of type D

### Andrew Schopieray

Interlochen, USA

## Abstract

Let $C(g,k)$ be the unitary modular tensor categories arising from the representation theory of quantum groups at roots of unity for arbitrary simple finite-dimensional complex Lie algebra $g$ and positive integer levels $k$. Here we classify nondegenerate fusion subcategories of the modular tensor categories of local modules $C(g,k)_{R}$ where $R$ is the regular algebra of Tannakian Rep$(H)⊂C(g,k)_{pt}$. We describe the decomposition of $C(g,k)_{R}$ into prime factors, and as an application we classify relations in the Witt group of nondegenerately braided fusion categories generated by the equivalency classes of $C(so_{5},k)$ and $C(g_{2},k)$ for $k∈Z_{≥1}$.

## Cite this article

Andrew Schopieray, Prime decomposition of modular tensor categories of local modules of type D. Quantum Topol. 11 (2020), no. 3, pp. 489–524

DOI 10.4171/QT/140