Resolutions over Koszul algebras
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2004
 arXiv:
 arXiv:math/0409162
 Bibcode:
 2004math......9162G
 Keywords:

 Rings and Algebras;
 Representation Theory;
 16S37;
 16E05;
 16W50
 EPrint:
 Arch. Math., 85 (2005), no. 2, 118127