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arXiv · 2608.18328

The Brauer category $\mathcal{B}(2)$ has principal graph $D_\infty$

Stephen Bigelow
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Abstract

We show that the subfactor planar algebra with principal graph $D_\infty$ is the Brauer planar algebra with bubble constant $\delta=2$. The Brauer algebra is similar to the Temperley-Lieb algebra, but with virtual crossings. At $\delta=2$, it relates to the category of representations of the orthogonal group $O(2)$. We work over any commutative ring with $1/2$. Its principal graph encodes information about the corresponding monoidal category.

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BibTeXRIS

Stephen Bigelow. 2026-08-18. The Brauer category $\mathcal{B}(2)$ has principal graph $D_\infty$. https://arxiv.org/abs/2608.18328

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