Orbit algebras and periodicity
Tom 114 / 2009
Colloquium Mathematicum 114 (2009), 245-252 MSC: 16B50, 16E05, 16E30, 16G60. DOI: 10.4064/cm114-2-7
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.