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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-2-7,
author = {Petter Andreas Bergh},
title = {Orbit algebras and periodicity},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {245-252},
zbl = {1187.16014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-2-7}
}
Petter Andreas Bergh. Orbit algebras and periodicity. Colloquium Mathematicae, Tome 116 (2009) pp. 245-252. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm114-2-7/