标题： 稳定同调同构对于分区和琼斯环代数 显示英文标题

标题： Stable homology isomorphisms for the partition and Jones annular algebras

摘要： 我们证明了在梯度为$\frac{1}{2}$的直线以下，琼斯环面代数的同调群与循环群的同调群同构。 我们也证明了在梯度为 1 的直线以下，分区代数的同调群与对称群的同调群同构，这加强了博伊德-赫普沃斯-帕特兹的结果。 这两个同构在超出相关代数稳定性范围的范围内均成立。 在此过程中，我们还证明了琼斯环面代数的标准奇数线和可逆参数结果。 显示英文摘要

摘要： We show that the homology of the Jones annular algebras is isomorphic to that of the cyclic groups below a line of gradient $\frac{1}{2}$. We also show that the homology of the partition algebras is isomorphic to that of the symmetric groups below a line of gradient 1, strengthening a result of Boyd-Hepworth-Patzt. Both isomorphisms hold in a range exceeding the stability range of the algebras in question. Along the way, we prove the usual odd-strand and invertible parameter results for the Jones annular algebras.