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Homological computations in the universal Steenrod algebra

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Ciampella A., Lomonaco L.

Fundamenta Mathematicae

2004

tom 183

nr 3

245-252

We study the (bigraded) homology of the universal Steenrod algebra Q over the prime field 𝔽₂, 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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1 Fundamenta Mathematicae

1 Ciampella A.

1 Lomonaco L.

1 2004

Wyniki wyszukiwania

Homological computations in the universal Steenrod algebra