Resolutions over Koszul algebras

Abstract

In this paper we show that if $\Lambda ={⨿}_{i\ge 0}{\Lambda }_i$ 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.

References in corpus (1)

• Finite Hochschild cohomology without finite global dimension