The hit problem of three variables for the cohomology of the classifying space BEs as a module over the mod 3 Steenrod Algebra at some low degrees

Abstract

The hit problem, set up by F. Peterson, finds a minimal set of generators for the polynomial algebra P(s)=F_2 [x_1,x_2,…,x_s ], as a module over the mod-2 Steenrod algebra. We study the extended hit problem for the cohomology of the classifying space 〖BE〗_s over field F_3, P(s)=H^* 〖B(RP^∞ )〗^s=E(x_1,x_2,…,x_s )⨂F_p [y_1,y_2,…,y_s ], with s=3 at degrees d ≤10.

Keywords

• Classifying space, exterior algebra, hit problem, polynomial algebra, Steenrod algebra