Complexity and periodicity

Petter Andreas Bergh. "Complexity and periodicity." Colloquium Mathematicae 104.2 (2006): 169-191. <http://eudml.org/doc/284189>.

@article{PetterAndreasBergh2006,
abstract = {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.},
author = {Petter Andreas Bergh},
journal = {Colloquium Mathematicae},
keywords = {eventually periodic modules; complexity; Hochschild cohomology; Artin algebras; syzygies; projective resolutions; sequences of Betti numbers; finitely generated modules; projective dimension},
language = {eng},
number = {2},
pages = {169-191},
title = {Complexity and periodicity},
url = {http://eudml.org/doc/284189},
volume = {104},
year = {2006},
}

TY - JOUR
AU - Petter Andreas Bergh
TI - Complexity and periodicity
JO - Colloquium Mathematicae
PY - 2006
VL - 104
IS - 2
SP - 169
EP - 191
AB - 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.
LA - eng
KW - eventually periodic modules; complexity; Hochschild cohomology; Artin algebras; syzygies; projective resolutions; sequences of Betti numbers; finitely generated modules; projective dimension
UR - http://eudml.org/doc/284189
ER -