Tensor algebras over the Steenrod algebra (Q6597173)

The paper investigates the structure of tensor algebras over the Steenrod algebra, extending previous results on polynomial algebras. It develops a method for decomposing the tensor algebra into ``weight spaces'' and applies the Dynkin-Specht-Weber theorem to obtain finer decompositions of these weight spaces. It then provides a method for computing the Hilbert series of the weight 0 subspace, with examples for \(N \leq 5\).\N\NIn conclusion, this paper makes a significant contribution to the understanding of tensor algebras over the Steenrod algebra. The extension of previous results from polynomial to tensor algebras is noteworthy, and the decomposition method presented is innovative. The computational examples for Hilbert series add practical value.