Geodesic
Homological computations in the universal Steenrod algebra
A. Ciampella1 ; L. A. Lomonaco1
1 Dipartimento di Matematica e Applicazioni Università di Napoli “Federico II” Napoli, Italy
Fundamenta Mathematicae, Tome 183 (2004) no. 3, pp. 245-252

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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].
DOI : 10.4064/fm183-3-4
Keywords: study bigraded homology universal steenrod algebra prime field mathbb compute groups using ideas techniques koszul algebras developed priddy although presently know whether koszul algebra provide explicit formula coalgebra structure diagonal homology * bigoplus * isomorphic coalgebra invariants mit gamma introduced singer

A. Ciampella 1 ; L. A. Lomonaco 1

1 Dipartimento di Matematica e Applicazioni Università di Napoli “Federico II” Napoli, Italy 
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A. Ciampella; L. A. Lomonaco. Homological computations in the universal
 Steenrod algebra. Fundamenta Mathematicae, Tome 183 (2004) no. 3, pp. 245-252. doi: 10.4064/fm183-3-4

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