Orbit algebras and periodicity

Volume 114 / 2009

Petter Andreas Bergh Colloquium Mathematicum 114 (2009), 245-252 MSC: 16B50, 16E05, 16E30, 16G60. DOI: 10.4064/cm114-2-7

Abstract

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.

Authors

  • Petter Andreas BerghInstitutt for matematiske fag
    NTNU
    N-7491 Trondheim, Norway
    e-mail

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