Homological computations in the universal Steenrod algebra

• Autorzy: A. Ciampella , L. A. Lomonaco
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 55T15: Adams spectral sequences
• 18G15: Ext and Tor, generalizations, K\"unneth formula
• 55S10: Steenrod algebra

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 183
• Numer: 3
• Strony: 245-252

Daty

wydano

2004

Twórcy

autor

A. Ciampella

• Dipartimento di Matematica e Applicazioni, Università di Napoli "Federico II", Napoli, Italy

autor

L. A. Lomonaco

• Dipartimento di Matematica e Applicazioni, Università di Napoli "Federico II", Napoli, Italy

Identyfikatory

DOI

10.4064/fm183-3-4