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arXiv · 1504.01895

Maximal green sequences for preprojective algebras

Magnus Engenhorst
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Abstract

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 \tau -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.

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Magnus Engenhorst. 2015-04-08. Maximal green sequences for preprojective algebras. https://arxiv.org/abs/1504.01895

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