Thick subcategories of finite algebraic triangulated categories

We classify the thick subcategories of an algebraic triangulated standard category with finitely many indecomposable objects.

💡 Research Summary

The paper addresses the problem of classifying thick subcategories in finite algebraic triangulated categories that are standard, i.e., Krull–Schmidt, Hom‑finite, k‑linear, and possess Auslander–Reiten triangles. Such categories arise as stable categories of Frobenius categories and, under the finiteness assumption, are known to be equivalent to orbit categories of bounded derived categories of Dynkin quivers, D⁽ᵇ⁾(kQ)/F, where F is a composition of the AR‑translation τ and the shift