A geometric description of m-cluster categories
 
 
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):
Date:  2008-03-17
Start Time:   15:00
Speaker:  Robert Marsh (University of Leeds)
Place:  5.5
Research Groups: -Algebra and Combinatorics
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