More on the anti-automorphism of the Steenrod algebra (Q640326)

The Adem relations in the Steenrod algebra can be expressed in many different ways. In particular, several relations have been published involving the product of a Steenrod power and the antipode of a Steenrod power, \({P}^i \chi({P}^{n-i})\) (where \({P}^i\) denotes \(Sq^i\) in the case \(p=2\)). A general family of linear relations of this type was given by \textit{M. G. Barratt} and \textit{H. R. Miller} [Contemp. Math. 12, 47--52 (1982; Zbl 0509.55011)] and \textit{M. C. Crabb} et al. [Proc. Am. Math. Soc. 124, No. 7, 2275--2281 (1996; Zbl 0864.55015)]. In the present paper, the authors determine a maximal set of such linear relations, and a basis for the space spanned by the elements \({P}^i \chi({P}^{n-i})\).