Brauer范畴$\boldsymbol{\textit{B}}(2)$的主图为$D_\boldsymbol{\textit{\textbackslash}infty}$
The Brauer category $\mathcal{B}(2)$ has principal graph $D_\infty$
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中文总结 AI 辅助
本研究证明主图为$D_\infty$的子因子平面代数是气泡常数$\delta=2$的Brauer平面代数，该代数与$O(2)$表示范畴相关，在含$1/2$的交换环上开展，其主图编码幺半范畴信息。
中文摘要 AI 辅助
我们证明了主图为$D_\boldsymbol{\textit{\textbackslash}infty}$的子因子平面代数是带气泡常数$\boldsymbol{\textit{\textbackslash}delta}=2$的Brauer平面代数。Brauer代数与Temperley-Lieb代数类似，但包含虚拟交叉。当$\boldsymbol{\textit{\textbackslash}delta}=2$时，它与正交群$\boldsymbol{\textit{\textit{O}}}(2)$的表示范畴相关，我们在任意含$1/2$的交换环上开展研究，其主图编码了对应幺半范畴的信息。
英文摘要
We show that the subfactor planar algebra with principal graph $D_\infty$ is the Brauer planar algebra with bubble constant $δ=2$. The Brauer algebra is similar to the Temperley-Lieb algebra, but with virtual crossings. At $δ=2$, 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.
