|
Description: |
[Joint work with Karin Baur (ETH, Zurich).]
Cluster categories are categories arising in the representation theory
of algebras as categorical models of Fomin-Zelevinsky cluster
algebras, which were introduced to study the multiplicative properties
of the dual canonical basis of a quantized enveloping algebra.
Their generalisations, m-cluster categories, model the m-cluster
combinatorics of Fomin-Reading.
A translation quiver is a graph together with a translation defined on
it. Key examples include the Auslander-Reiten quivers of finite
dimensional algebras. We show that there is a natural notion of the mth
power of a translation quiver which is again a translation quiver.
We use this to give a geometric description of m-cluster categories of
types A and D in terms of arcs in a disc, using the geometric
construction of cluster categories of types A (Caldero-Chapoton-Schiffler)
and D (Schiffler).
Area(s):
|
