The Arnon bases in the Steenrod algebra
Articles > Article · 2018
Authors: Neset Deniz Turgay, İsmet KARACA
Georgian Mathematical Journal, Journal Indexed in SCI Expanded, International, WoS, 2018, vol 27, pp 649-654
Summary
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}} .