The Derived Category of Surface Algebras: the Case of the Torus with One Boundary Component

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• 作者：Claire Amiot
• 关键词：Quiver representation ; Derived categories ; Triangulations of surfaces ; Cluster combinatorics ; Quiver mutation
• 刊名：Algebras and Representation Theory
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：19
• 期：5
• 页码：1059-1080
• 全文大小：1,495 KB
• 刊物主题：Commutative Rings and Algebras; Associative Rings and Algebras; Non-associative Rings and Algebras;
• 出版者：Springer Netherlands
• ISSN：1572-9079
• 卷排序：19

文摘

In this paper we refine the main result of a previous paper of the author with Grimeland on derived invariants of surface algebras. We restrict to the case where the surface is a torus with one boundary component and give an easily computable derived invariant for such surface algebras. This result permits to give answers to open questions on gentle algebras: it provides examples of gentle algebras with the same AG-invariant (in the sense of Avella-Alaminos and Geiss) that are not derived equivalent and gives a partial positive answer to a conjecture due to Bobiński and Malicki on gentle 2-cycle algebras.