We study the (bigraded) homology of the universal Steenrod algebra Q over the prime field F2, and we compute the groups Hs,s(Q), s≥0, using some ideas and techniques of Koszul algebras developed by S. Priddy, 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≥0Hs,s(Q) and show that D∗(Q) is isomorphic to the coalgebra of invariants Γ introduced by W. Singer.
Homological computations in the universal Steenrod algebra / Ciampella, Adriana; Lomonaco, LUCIANO AMITO. - In: FUNDAMENTA MATHEMATICAE. - ISSN 0016-2736. - STAMPA. - 183:(2004), pp. 245-252.
Homological computations in the universal Steenrod algebra
CIAMPELLA, ADRIANA;LOMONACO, LUCIANO AMITO
2004
Abstract
We study the (bigraded) homology of the universal Steenrod algebra Q over the prime field F2, and we compute the groups Hs,s(Q), s≥0, using some ideas and techniques of Koszul algebras developed by S. Priddy, 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≥0Hs,s(Q) and show that D∗(Q) is isomorphic to the coalgebra of invariants Γ introduced by W. Singer.| File | Dimensione | Formato | |
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