Auslander-Reiten conjecture for symmetric algebras of polynomial growth

Guodong Zhou (1) , Alexander Zimmermann (2)

1 University of Paderborn
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

This paper studies self-injective algebras of polynomial growth. We prove that the derived equivalence classification of weakly symmetric algebras of domestic type coincides with the classification up to stable equivalences (of Morita type). As for weakly symmetric non-domestic algebras of polynomial growth, up to some scalar problems, the derived equivalence classification coincides with the classification up to stable equivalences of Morita type. As a consequence, we get the validity of the Auslander-Reiten conjecture for stable equivalences of Morita type between weakly symmetric algebras of polynomial growth.

Domaines: Théorie des représentations [math.RT]; Anneaux et algèbres [math.RA]

Guodong Zhou, Alexander Zimmermann. Auslander-Reiten conjecture for symmetric algebras of polynomial growth. Beitraege Zur Algebra Und Geometrie, 2011, 53 (2), pp.349 - 364. ⟨hal-00481414⟩