Koszul resolutions

Priddy, Stewart B.

doi:10.1090/S0002-9947-1970-0265437-8

Koszul resolutions
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by Stewart B. Priddy

Trans. Amer. Math. Soc. 152 (1970), 39-60

DOI: https://doi.org/10.1090/S0002-9947-1970-0265437-8

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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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