Let ${\mathrm{\Gamma }}^{(x_0)}$ be a finite rooted tree, for which Γ is the underlying tree and $x_0$ the root. Let T be the Terwilliger algebra of Γ with respect to $x_0$. We study the structure of the principal T-module. As a result, it is shown that T recognizes the isomorphism class of ${\mathrm{\Gamma }}^{(x_0)}$.

中文翻译：

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从Terwilliger代数的角度看树木的同构问题

让 ${\mathrm{\Gamma }}^{（X_0）}$ 是有限根树，其中Γ是基础树， $X_0$根。设T为Γ的Terwilliger代数$X_0$。我们研究了主要T模块的结构。结果表明，T识别出${\mathrm{\Gamma }}^{（X_0）}$。