Homological computations in the universal Steenrod algebra

A. Ciampella, and L. A. Lomonaco. "Homological computations in the universal Steenrod algebra." Fundamenta Mathematicae 183.3 (2004): 245-252. <http://eudml.org/doc/283351>.

@article{A2004,
abstract = {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].},
author = {A. Ciampella, L. A. Lomonaco},
journal = {Fundamenta Mathematicae},
keywords = {Koszul algebras; homology of algebras; universal Steenrod algebra},
language = {eng},
number = {3},
pages = {245-252},
title = {Homological computations in the universal Steenrod algebra},
url = {http://eudml.org/doc/283351},
volume = {183},
year = {2004},
}

TY - JOUR
AU - A. Ciampella
AU - L. A. Lomonaco
TI - Homological computations in the universal Steenrod algebra
JO - Fundamenta Mathematicae
PY - 2004
VL - 183
IS - 3
SP - 245
EP - 252
AB - 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].
LA - eng
KW - Koszul algebras; homology of algebras; universal Steenrod algebra
UR - http://eudml.org/doc/283351
ER -