The Arnon bases in the Steenrod algebra

Abstract

Let A = A(p) be the mod p Steenrod algebra, where p is a fixed prime and let A' denote the Bockstein-free part of A at odd primes. Being a connected graded Hopf algebra, A has the canonical conjugations. Using this map, we introduce a relationship between the X- and Z-bases of A'. We show that these bases restrict to give bases to the well-known sub-Hopf algebras A(n - 1), n >= 1, of A'.