Abstract
Resolutions, which generalize the classical Koszul resolutions, are constructed for a large class of augmented algebras including the Steenrod algebra and the universal enveloping algebras. For each such algebra $A$, an explicit differential algebra $\bar K\ast (A)$ is described such that (1) $\bar K^ \ast (A)$ is a small quotient algebra of the cobar complex and (2) the homology of $\bar K^ \ast (A)$ is the cohomology algebra $H ^ \ast (A)$. The resolution of May for restricted Lie algebras in characteristic 2 is retrieved and a simple derivation of the resolution of Kan et al. of the Steenrod algebra is given.
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