The Arnon bases in the Steenrod algebra
Makaleler > Tam Makale · 2018
Yazarlar: Neset Deniz Turgay, İsmet KARACA
Georgian Mathematical Journal, SCI Expanded İndekslerine Giren Dergi, Uluslararası, Wos, 2018, cilt 27, ss 649-654
Özet
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}} .