{"language":[{"iso":"eng"}],"_id":"66859","user_id":"64242","author":[{"id":"72064","first_name":"Igor","last_name":"Burban","full_name":"Burban, Igor"},{"id":"64242","full_name":"Perniok, Daniel","first_name":"Daniel","last_name":"Perniok"}],"status":"public","title":"Double Hall algebras and derived equivalences revisited","year":"2026","date_updated":"2026-08-26T12:15:11Z","date_created":"2026-08-26T12:08:41Z","external_id":{"arxiv":["2608.24331"]},"type":"preprint","citation":{"short":"I. Burban, D. Perniok, (2026).","chicago":"Burban, Igor, and Daniel Perniok. “Double Hall Algebras and Derived Equivalences Revisited,” 2026.","apa":"Burban, I., &#38; Perniok, D. (2026). <i>Double Hall algebras and derived equivalences revisited</i>.","ieee":"I. Burban and D. Perniok, “Double Hall algebras and derived equivalences revisited.” 2026.","ama":"Burban I, Perniok D. Double Hall algebras and derived equivalences revisited. Published online 2026.","bibtex":"@article{Burban_Perniok_2026, title={Double Hall algebras and derived equivalences revisited}, author={Burban, Igor and Perniok, Daniel}, year={2026} }","mla":"Burban, Igor, and Daniel Perniok. <i>Double Hall Algebras and Derived Equivalences Revisited</i>. 2026."},"abstract":[{"text":"Let $\\mathbb{k}$ be a finite field and $\\mathcal{A}, \\mathcal{B}$ be $\\mathbb{k}$-linear $\\mathsf{Ext}$-finite hereditary abelian categories. A theorem of Cramer asserts that, under suitable assumptions, a derived equivalence $\\mathcal{D}^b(\\mathcal{A}) \\!\\longrightarrow\\! \\mathcal{D}^b(\\mathcal{B})$ between two such categories induces an algebra isomorphism of the corresponding double Hall algebras $\\mathsf{DH}_\\mathcal{A} \\!\\longrightarrow\\! \\mathsf{DH}_\\mathcal{B}$. It turns out that a counting formula for certain distinguished triangles in $\\mathcal{D}^b(\\mathcal{A})$, on which Cramer's proof relies, is incorrect in general. We give a corrected proof of Cramer's theorem which preserves the overall strategy of his approach.","lang":"eng"}]}