Homological computations in the universal Steenrod algebra
Volume 183 / 2004
Fundamenta Mathematicae 183 (2004), 245-252
MSC: 55S10, 18G15, 55T15.
DOI: 10.4064/fm183-3-4
Abstract
We study the (bigraded) homology of the universal Steenrod algebra $Q$ over the prime field ${{\mathbb F}}_2$, and we compute the groups $H_{s,s}(Q)$, $s\ge 0$, using some ideas and techniques of Koszul algebras developed by S. Priddy in [5], although we presently do not know whether or not $Q$ is a Koszul algebra. We also provide an explicit formula for the coalgebra structure of the diagonal homology $D_*(Q)=\bigoplus _{s\ge 0}H_{s,s}(Q)$ and show that $D_*(Q)$ is isomorphic to the coalgebra of invariants ${\mit \Gamma }$ introduced by W. Singer in [6].
