# Resolutions of mesh algebras: periodicity and Calabi-Yau dimensions - Mathematics > Representation Theory

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Abstract: A triangulated category is said to be Calabi-Yau of dimension d if the dthpower of its suspension is a Serre functor. We determine which stablecategories of self-injective algebras A of finite representation type areCalabi-Yau and compute their Calabi-Yau dimensions. We achieve this by studyingthe minimal projective resolution of the stable Auslander algebra of A over itsenveloping algebra, and use covering theory to reduce to generalizedpreprojective algebras of Dynkin graphs. We also describe how this problem canbe approached by realizing the stable categories in question as orbitcategories of the bounded derived categories of hereditary algebras.

Author: ** Alex Dugas**

Source: https://arxiv.org/