Complexity and periodicity
Tom 104 / 2006
Colloquium Mathematicum 104 (2006), 169-191
MSC: Primary 16E05, 16E40, 16P10, 16P20, 16P90; Secondary 20J06.
DOI: 10.4064/cm104-2-2
Streszczenie
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.