Complexity and periodicity

• Autorzy: Petter Andreas Bergh
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16P90: Growth rate, Gelfand-Kirillov dimension
• 16P20: Artinian rings and modules
• 16P10: Finite rings and finite-dimensional algebras
• 20J06: Cohomology of groups
• 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
• 16E05: Syzygies, resolutions, complexes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 104
• Numer: 2
• Strony: 169-191

Daty

wydano

2006

Twórcy

autor

Petter Andreas Bergh

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

Identyfikatory

DOI

10.4064/cm104-2-2