Resolutions of mesh algebras: periodicity and Calabi-Yau dimensions

Abstract

A triangulated category is said to be Calabi-Yau of dimension d if the dth power of its suspension is a Serre functor. We determine which stable categories of self-injective algebras A of finite representation type are Calabi-Yau and compute their Calabi-Yau dimensions. We achieve this by studying the minimal projective resolution of the stable Auslander algebra of A over its enveloping algebra, and use covering theory to reduce to (generalized) preprojective algebras of Dynkin graphs. We also describe how this problem can be approached by realizing the stable categories in question as orbit categories of the bounded derived categories of hereditary algebras.

Final version. To appear in Math. Z

References in corpus (1)

• On triangulated orbit categories

Cited by in corpus (9)

• 2-CY-tilted algebras that are not Jacobian
• Spherical subcategories in algebraic geometry
• Stable Calabi--Yau dimension of self-injective algebras of finite type
• The Grothendieck groups and stable equivalences of mesh algebras
• Deformed mesh algebras of Dynkin type ${\mathbb{F}}_4$
• Stably Calabi-Yau properties of derivation quotient algebras
• Hochschild cohomology for periodic algebras of polynomial growth
• Realizing orbit categories as stable module categories - a complete classification
• Tate Duality and Transfer for Symmetric Algebras Over Complete Discrete Valuation Rings