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Transactions of the American Mathematical Society

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Koszul resolutions


Author: Stewart B. Priddy
Journal: Trans. Amer. Math. Soc. 152 (1970), 39-60
MSC: Primary 18.20
DOI: https://doi.org/10.1090/S0002-9947-1970-0265437-8
MathSciNet review: 0265437
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0265437-8
Keywords: Koszul resolutions, bar and cobar resolutions, cohomology of the Steenrod algebra, cohomology of Lie algebras
Article copyright: © Copyright 1970 American Mathematical Society

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