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Complexity and periodicity

100%

Bergh P.

Colloquium Mathematicum

2006

tom 104

nr 2

169-191

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.

Orbit algebras and periodicity

100%

Bergh P.

Colloquium Mathematicum

2009

tom 114

nr 2

245-252

Given an object in a category, we study its orbit algebra with respect to an endofunctor. We show that if the object is periodic, then its orbit algebra modulo nilpotence is a polynomial ring in one variable. This specializes to a result on Ext-algebras of periodic modules over Gorenstein algebras. We also obtain a criterion for an algebra to be of wild representation type.

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2 Colloquium Mathematicum

2 Bergh P.

1 2009

1 2006

Wyniki wyszukiwania

Complexity and periodicity

Orbit algebras and periodicity