Maximal Green Sequences for Preprojective Algebras

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• 作者：Magnus Engenhorst
• 关键词：Preprojective algebra ; Maximal green sequences ; Finite ; dimensional algebras ; Triangulated categories
• 刊名：Algebras and Representation Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：20
• 期：1
• 页码：163-174
• 全文大小：
• 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：20

文摘

Maximal green sequences were introduced as combinatorical counterpart for Donaldson-Thomas invariants for 2-acyclic quivers with potential by B. Keller. We take the categorical notion and introduce maximal green sequences for hearts of bounded t-structures of triangulated categories that can be tilted indefinitely. We study the case where the heart is the category of modules over the preprojective algebra of a quiver without loops. The combinatorical counterpart of maximal green sequences for Dynkin quivers are maximal chains in the Hasse quiver of basic support τ-tilting modules. We show that a quiver has a maximal green sequence if and only if it is of Dynkin type. More generally, we study module categories for finite-dimensional algebras with finitely many bricks.