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 (2)

• Multiplicative structures for Koszul algebras
• Finite Hochschild cohomology without finite global dimension

Cited by in corpus (7)

• Multiplicative structures for Koszul algebras
• Support varieties and the Hochschild cohomology ring modulo nilpotence
• Hochschild cohomology and support varieties for tame Hecke algebras
• On the Hochschild cohomology of tame Hecke algebras
• A family of Koszul self-injective algebras with finite Hochschild cohomology
• Cup product on Hochschild cohomology of a family of quiver algebras
• On Hochschild cohomology of a self-injective special biserial algebra obtained by a circular quiver with double arrows