Resolutions over Koszul algebras

Details Resolutions over Koszul algebras Resolutions over Koszul algebras

2004-09-09

arxiv.org/abs/math/0409162v1

Arch. Math., 85 (2005), no. 2, 118-127

Mathematics

Rings and Algebras

Scientific paper

10.1007/s00013-005-1299-9

In this paper we show that if $\Lambda=\amalg_{i\geq 0}\Lambda_i$ is a Koszul algebra with $\Lambda_0$ isomorphic to a product of copies of a field, then the minimal projective resolution of $\Lambda_0$ as a right $\Lambda$-module provides all the information necessary to construct both a minimal projective resolution of $\Lambda_0$ as a left $\Lambda$-module and a minimal projective resolution of $\Lambda$ as a right module over the enveloping algebra of $\Lambda$. The main tool for this is showing that there is a comultiplicative structure on a minimal projective resolution of $\Lambda_0$ as a right $\Lambda$-module.

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