On tropical friezes associated with Dynkin diagrams

Mathematics – Representation Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

27pages, reference to J. Propp's work added

Scientific paper

Tropical friezes are the tropical analogues of Coxeter-Conway frieze patterns. In this note, we study them using triangulated categories. A tropical frieze on a 2-Calabi-Yau triangulated category $\mathcal{C}$ is a function satisfying a certain addition formula. We show that when $\mathcal{C}$ is the cluster category of a Dynkin quiver, the tropical friezes on ${\mathcal{C}}$ are in bijection with the $n$-tuples in ${\mathbb{Z}}^n$, any tropical frieze $f$ on $\mathcal{C}$ is of a special form, and there exists a cluster-tilting object such that $f$ simultaneously takes non-negative values or non-positive values on all its indecomposable direct summands. Using similar techniques, we give a proof of a conjecture of Ringel for cluster-additive functions on stable translation quivers.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

On tropical friezes associated with Dynkin diagrams does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On tropical friezes associated with Dynkin diagrams, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On tropical friezes associated with Dynkin diagrams will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-643609

All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.