Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6414150 | Journal of Algebra | 2017 | 30 Pages |
Abstract
We use semi-invariant pictures to prove two conjectures about maximal green sequences. First: if Q is any acyclic valued quiver with an arrow jâi of infinite type then any maximal green sequence for Q must mutate at i before mutating at j. Second: for any quiver Qâ² obtained by mutating an acyclic valued quiver Q of tame type, there are only finitely many maximal green sequences for Qâ². Both statements follow from the Rotation Lemma for reddening sequences and this in turn follows from the Mutation Formula for the semi-invariant picture for Q.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Thomas Brüstle, Stephen Hermes, Kiyoshi Igusa, Gordana Todorov,