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Homological computations in the universal Steenrod algebra

A. Ciampella, L. A. Lomonaco (2004)

Fundamenta Mathematicae

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].

Homomorphic images and rationalizations based on the Eilenberg-MacLane spaces

Dae-Woong Lee (2005)

Czechoslovak Mathematical Journal

Are there any kinds of self maps on the loop structure whose induced homomorphic images are the Lie brackets in tensor algebra? We will give an answer to this question by defining a self map of Ω Σ K ( , 2 d ) , and then by computing efficiently some self maps. We also study the topological rationalization properties of the suspension of the Eilenberg-MacLane spaces. These results will be playing a powerful role in the computation of the same n -type problems and giving us an information about the rational homotopy...

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