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

Let H be a bialgebra. An H-module-algebra is an associative algebra A that is also an H-module such that the multiplication map on A becomes an H-module morphism. This algebraic structure arises often in algebraic topology, quantum groups [11, Chapter V.6], Lie and Hopf algebras theory [3, 16, 19], and group representations [1, Chapter 3]. For example, in algebraic topology, the complex cobordi...