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arXiv · 1904.09247

A survey on maximal green sequences

Laurent Demonet·Bernhard Keller
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Abstract

Maximal green sequences appear in the study of Fomin-Zelevinsky's cluster algebras. They are useful for computing refined Donaldson-Thomas invariants, constructing twist automorphisms and proving the existence of theta bases and generic bases. We survey recent progress on their existence and properties and give a representation-theoretic proof of Greg Muller's theorem stating that full subquivers inherit maximal green sequences. In the appendix, Laurent Demonet describes maximal chains of torsion classes in terms of bricks generalizing a theorem by Igusa.

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Laurent Demonet, Bernhard Keller. 2020-12-01. A survey on maximal green sequences. https://arxiv.org/abs/1904.09247

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