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Homological computations in the universal Steenrod algebra

A. CiampellaL. A. Lomonaco — 2004

Fundamenta Mathematicae

We study the (bigraded) homology of the universal Steenrod algebra Q over the prime field ₂, and we compute the groups H s , s ( Q ) , s ≥ 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 ) = s 0 H s , s ( Q ) and show that D⁎(Q) is isomorphic to the coalgebra of invariants Γ introduced by W. Singer in [6].

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