[PDF][PDF] From finite to infinite: cluster algebras as colimits, and mutating torsion pairs in discrete cluster categrories
SH Gratz - 2015 - repo.uni-hannover.de
2015•repo.uni-hannover.de
This thesis explores some questions regarding the combinatorial structure of cluster
algebras and cluster categories, with a strong focus on cluster algebras and cluster
categories of infinite rank. Recently, cluster algebras of infinite rank have received more and
more attention. We formalize the way in which one can think about cluster algebras of infinite
rank by showing that every rooted cluster algebra of infinite rank can be written as a colimit
of rooted cluster algebras of finite rank. Relying on the proof of the positivity conjecture for …
algebras and cluster categories, with a strong focus on cluster algebras and cluster
categories of infinite rank. Recently, cluster algebras of infinite rank have received more and
more attention. We formalize the way in which one can think about cluster algebras of infinite
rank by showing that every rooted cluster algebra of infinite rank can be written as a colimit
of rooted cluster algebras of finite rank. Relying on the proof of the positivity conjecture for …
Abstract
This thesis explores some questions regarding the combinatorial structure of cluster algebras and cluster categories, with a strong focus on cluster algebras and cluster categories of infinite rank.
Recently, cluster algebras of infinite rank have received more and more attention. We formalize the way in which one can think about cluster algebras of infinite rank by showing that every rooted cluster algebra of infinite rank can be written as a colimit of rooted cluster algebras of finite rank. Relying on the proof of the positivity conjecture for skew-symmetric cluster algebras of finite rank by Lee and Schiffler, it follows as a direct consequence that the positivity conjecture holds for skew-symmetric cluster algebras of infinite rank.
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