Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 18.20

Retrieve articles in all journals with MSC: 18.20


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