For the remaining ones, i.e., those selfinjective algebras whose stable categories are actually Calabi-Yau, the difference between the Calabi-Yau dimensions of the indecomposable Calabi-Yau objects and the Calabi-Yau dimensions of the stable categories is described. For selfinjective algebras with such properties, the ones whose stable categories are not Calabi-Yau are determined. These Gromov-Witten type invariants depend on a Calabi-Yau A category, which plays the role of the target in ordinary Gromov-Witten theory. The authors give a discription of the stable categories of selfinjective algebras of finite representation type over an algebraically closed field, which admits indecomposable Calabi-Yau obdjects. Calabi-Yau structures on dg-categories Asked 2 years, 4 months ago Modified 2 years, 4 months ago Viewed 162 times 5 A (smooth) dg algebra is called (left) Calabi-Yau if (see for example here ) A A n Here we use the inverse dualizing complex A R Hom ( A e) o p ( A, A e). This is the first of two papers which construct a purely algebraic counterpart to the theory of Gromov-Witten invariants (at all genera). We prove a structure theorem for triangulated CalabiYau categories: an algebraic 2-CalabiYau triangulated category over an algebraically closed field is a. Indecomposable Calabi-Yau objects in stable module categories of finite type Indecomposable Calabi-Yau objects in stable module categories of finite type
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