标题： 关于$\mathrm{Ext}_{\mathcal A}^{k,k+*}(\mathbb{Z}/2,\mathbb{Z}/2)$的计算对于$k \leq 5$ 显示英文标题

标题： On the computation of $\mathrm{Ext}_{\mathcal A}^{k,k+*}(\mathbb{Z}/2,\mathbb{Z}/2)$ for $k \leq 5$

摘要： 本简报提出了一种计算算法，用于确定模2 Steenrod 代数的上同调基，$\mathrm{Ext}_{\mathcal A}^{k, k+*}(\mathbb{Z}/2, \mathbb{Z}/2)$对于$k \leq 5$，基于Chen的工作[2]中给出的已知生成元和Adem关系。 该算法的目的是验证我们在修正论文[8, 9, 10]中手工计算的$\mathrm{Ext}_{\mathcal A}^{4, 4+*}(\mathbb{Z}/2, \mathbb{Z}/2)$结果。 结合我们最近的工作[11, 12]，现在可以完成特定次数中第四代数转移的定义域和陪域的验证。 显示英文摘要

摘要： This Note presents a computational algorithm for determining a basis of the cohomology of the mod 2 Steenrod algebra, $\mathrm{Ext}_{\mathcal A}^{k, k+*}(\mathbb{Z}/2, \mathbb{Z}/2)$ for $k \leq 5$, based on the well-known generators and the Adem relations given in Chen's work [2]. The purpose of this algorithm is to verify the hand-computed results for $\mathrm{Ext}_{\mathcal A}^{4, 4+*}(\mathbb{Z}/2, \mathbb{Z}/2)$ presented in our corrected papers [8, 9, 10]. Combining our most recent works [11, 12], the verification of the domain and the codomain of the fourth algebraic transfer in specific degrees can now be completed.