Sira Gratz (Hannover): Cluster algebras of infinite rank as colimits (Oberseminar Algebra und Geometrie)
Wednesday, 16.04.2014 15:00 im Raum N 2
Assem, Dupont and Schier introduced the category of rooted cluster
algebras, which has as objects pairs (A; ), where A is a cluster algebra
(of possibly innite rank) and a distinguished initial seed of A. We show
that, though the category of rooted cluster algebras does not in general
admit colimits, every rooted cluster algebra can be written as a directed
colimit of rooted cluster algebras of nite rank. Directed colimits of rooted
cluster algebras of Dynkin type A have a geometric interpretation as tri-
angulations of the closed disc with innitely many marked points on the
boundary. They are related to innite discrete cluster categories of type
A, respectively the continuous cluster category of type A as introduced
by Igusa and Todorov.
Angelegt am Monday, 14.04.2014 07:55 von N. N
Geändert am Monday, 14.04.2014 07:58 von N. N
[Edit | Vorlage]