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Resolutions over Koszul algebras

E. L. Green·G. Hartman·E. N. Marcos·Ø. Solberg
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Abstract

In this paper we show that if $Λ=\amalg_{i\geq 0}Λ_i$ is a Koszul algebra with $Λ_0$ isomorphic to a product of copies of a field, then the minimal projective resolution of $Λ_0$ as a right $Λ$-module provides all the information necessary to construct both a minimal projective resolution of $Λ_0$ as a left $Λ$-module and a minimal projective resolution of $Λ$ as a right module over the enveloping algebra of $Λ$. The main tool for this is showing that there is a comultiplicative structure on a minimal projective resolution of $Λ_0$ as a right $Λ$-module.

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BibTeXRIS

E. L. Green, G. Hartman, E. N. Marcos, Ø. Solberg. 2004-09-09. Resolutions over Koszul algebras. https://doi.org/10.1007/s00013-005-1299-9

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