超立方体的广义Terwilliger代数
The Generalized Terwilliger Algebra of the Hypercube
摘要：
2000年，Eric Egge引入了距离正则图$Γ$的广义Terwilliger代数$\mathcal T$.对于$Γ,$的任何顶点$x$，都存在从$\mathcal T$到Terwilliger代数$T(x)$的满射代数同态$\natural$。如果$Γ$是完备的，则$\natural$是同构。如果$Γ$不完整，那么$\natural$可能是也可能不是同构，一般来说细节是未知的。证明了若$Γ$是超立方体，则代数同态$\natural:\mathcal T \to T(x)$是$Γ$的所有顶点$x$的同构.
英文摘要：
In the year 2000, Eric Egge introduced the generalized Terwilliger algebra $\mathcal T$ of a distance-regular graph $Γ$. For any vertex $x$ of $Γ,$ there is a surjective algebra homomorphism $\natural$ from $\mathcal T$ to the Terwilliger algebra $T(x)$. If $Γ$ is complete, then $\natural$ is an isomorphism. If $Γ$ is not complete, then $\natural$ may or may not be an isomorphism, and in general the details are unknown. We show that if $Γ$ is a hypercube, then the algebra homomorphism $\natural:\mathcal T \to T(x)$ is an isomorphism for all vertices $x$ of $Γ$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
