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arXiv · 2608.20465

On the Drinfeld center of the Verlinde category $\Ver_p$

Shlomo Gelaki·Victor Ostrik
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Abstract

We provide some information about the Drinfeld center $\Z(\Ver_p)$ of the Verlinde category $\Ver_p$. We compute explicitly the Cartan matrix, bound quiver and cohomology of $\Z(\Ver_p^+)$, and prove that the category $\mathscr{Z}(\Ver_p^+)$ is wild for every $p\ge 7$. In the special case $p=5$, we show that $\Z(\Ver_5^+)$ has exactly $10$ non-isomorphic indecomposable objects, classify them and describe the Green ring of $\Z(\Ver_5^+)$, and compute the semisimplification of $\Z(\Ver_5^+)$.

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Shlomo Gelaki, Victor Ostrik. 2026-08-20. On the Drinfeld center of the Verlinde category $\Ver_p$. https://arxiv.org/abs/2608.20465

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