Generic bases for cluster algebras from the cluster category

Details Generic bases for cluster algebras from the cluster category Generic bases for cluster algebras from the cluster category

2011-11-18

arxiv.org/abs/1111.4431v2

Mathematics

Representation Theory

36 pages, changes in the presentation for v2

Scientific paper

Inspired by recent work of Geiss-Leclerc-Schroer, we use Hom-finite cluster categories to give a good candidate set for a basis of (upper) cluster algebras with coefficients arising from quivers. This set consists of generic values taken by the cluster character on objects having the same index. If the matrix associated to the quiver is of full rank, then we prove that the elements in this set are linearly independent. If the cluster algebra arises from the setting of Geiss-Leclerc-Schroer, then we obtain the basis found by these authors. We show how our point of view agrees with the spirit of conjectures of Fock-Goncharov concerning the parametrization of a basis of the upper cluster algebra by points in the tropical X-variety.

Affiliated with

Also associated with

No associations

Rating

Generic bases for cluster algebras from the cluster category 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 Generic bases for cluster algebras from the cluster category, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generic bases for cluster algebras from the cluster category will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-549831