Abstract Let 𝒜 = 𝒜 p {\mathcal{A}=\mathcal{A}_{p}} be the mod ⁢ p {\mathrm{mod}\,p} Steenrod algebra, where p is a fixed prime and let 𝒜 ′ {\mathcal{A}^{\prime}} denote the Bockstein-free part of 𝒜 {\mathcal{A}} at odd primes. Being a connected graded Hopf algebra, 𝒜 {\mathcal{A}} has the canonical conjugation χ. Using this map, we introduce a relationship between the X- and Z-bases of 𝒜 ′ {\mathcal{A}^{\prime}} . We show that these bases restrict to give bases to the well-known sub-Hopf algebras 𝒜 ⁢ ( n - 1 ) {\mathcal{A}(n-1)} , n ≥ 1 {n\geq 1} , of 𝒜 ′ {\mathcal{A}^{\prime}} .

中文翻译：

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Steenrod 代数中的 Arnon 基

摘要 令 𝒜 = 𝒜 p {\mathcal{A}=\mathcal{A}_{p}} 是 mod ⁢ p {\mathrm{mod}\,p} Steenrod 代数，其中 p 是固定素数，令 𝒜 ′ {\mathcal{A}^{\prime}} 表示 𝒜 {\mathcal{A}} 在奇素数处的 Bockstein-free 部分。作为连通分级 Hopf 代数，𝒜 {\mathcal{A}} 具有规范共轭 χ。使用这张地图，我们引入了 𝒜 ′ {\mathcal{A}^{\prime}} 的 X 和 Z 基之间的关系。我们证明这些基数限制为众所周知的 sub-Hopf 代数 𝒜 ⁢ ( n - 1 ) {\mathcal{A}(n-1)} , n ≥ 1 {n\geq 1} , of 𝒜 ′ {\mathcal{A}^{\prime}} 。