On a minimal set of generators for the algebra H ∗ ( B E d ; F 2 ) and its applications

Abstract

We investigate the Peterson hit problem for the polynomial algebra \(\mathcal P_{d}\), viewed as a graded left module over the mod-\(2\) Steenrod algebra, \(\mathcal{A}\). For \(d>4\), this problem is still unsolved, even in the case of \(d=5\) with the help of computers. In this article, we study the hit problem for the case \(d=6\) in the generic degree \(6(2^{r}-1)+6.2^r\), with \(r\) an arbitrary non-negative integer. Furthermore, the behavior of the sixth Singer algebraic transfer in degree \(6(2^{r}-1)+6.2^r\) is also discussed at the end of this paper.