Year: 2026
Type: article
Abstract: We work over a perfect field. In this article, given an integer d ≥ 1 d\geq 1 , we establish a bijection between twisted ( d + 2 ) (d+2) -periodic algebras and suitable algebraic triangulated categories with a d Z d\mathbb {Z} -cluster tilting object. Furthermore, we show that these triangulated categories admit a unique differential graded enhancement. Our result yields recognition theorems for interesting algebraic triangulated categories, such as the Amiot cluster category of a self-injective quiver with potential in the sense of Herschend and Iyama and, more generally, the Amiot–Guo–Keller cluster category associated with a d d -representation finite algebra in the sense of Iyama and Oppermann. As an application of our result, we obtain infinitely many triangulated categories with a unique differential graded enhancement that is not strongly unique. In the appendix, B. Keller explains how—combined with crucial results of August and Hua–Keller—our main result yields the last key ingredient to prove the Donovan–Wemyss Conjecture in the context of the Homological Minimal Model Program for threefolds.
DOI: 10.1090/jams/1079
Authors: Gustavo Jasso, Fernando Muro
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1192812326, G1265117388, EXC 2047: Hausdorff Center for Mathematics (HCM), G2201736333, G2256575167, G2467073444, G3419232337, G3895380366, G3919009022, G4663364688, G4666241883, G4844358548, G4871223410, G5190686154, G5892737577, G6264776348, G6318096328, G640844427, G6572250646, G7922655386, G7923750194, G8208290308, G8545594460, G855360370, Clusters, Homological Algebra, Representations and Mirror Symmetry
OpenAlex ID: W7161840241