Complexity and periodicity

Petter Andreas Bergh¹

¹ Institutt for matematiske fag NTNU N-7491 Trondheim, Norway

Colloquium Mathematicum, Tome 104 (2006) no. 2, pp. 169-191

Résumé

Let $M$ be a finitely generated module over an Artin algebra. By considering the lengths of the modules in the minimal projective resolution of $M$, we obtain the Betti sequence of $M$. This sequence must be bounded if $M$ is eventually periodic, but the converse fails to hold in general. We give conditions under which it holds, using techniques from Hochschild cohomology. We also provide a result which under certain conditions guarantees the existence of periodic modules. Finally, we study the case when an element in the Hochschild cohomology ring “generates” the periodicity of a module.

Détail

DOI : 10.4064/cm104-2-2

Keywords: finitely generated module artin algebra considering lengths modules minimal projective resolution obtain betti sequence sequence bounded eventually periodic converse fails general conditions under which holds using techniques hochschild cohomology provide result which under certain conditions guarantees existence periodic modules finally study element hochschild cohomology ring generates periodicity module