Complexity and periodicity

Tom 104 / 2006

Petter Andreas Bergh Colloquium Mathematicum 104 (2006), 169-191 MSC: Primary 16E05, 16E40, 16P10, 16P20, 16P90; Secondary 20J06. DOI: 10.4064/cm104-2-2


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.


  • Petter Andreas BerghInstitutt for matematiske fag
    N-7491 Trondheim, Norway

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