Quivers with relations and cluster tilted algebras

Details Quivers with relations and cluster tilted algebras Quivers with relations and cluster tilted algebras

2004-11-10

arxiv.org/abs/math/0411238v1

Mathematics

Representation Theory

19 pages, 3 figures

Scientific paper

Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. To a cluster algebra of simply laced Dynkin type one can associate the cluster category. Any cluster of the cluster algebra corresponds to a tilting object in the cluster category. The cluster tilted algebra is the algebra of endomorphisms of that tilting object. Viewing the cluster tilted algebra as a path algebra of a quiver with relations, we prove in this paper that the quiver of the cluster tilted algebra is equal to the cluster diagram. We study also the relations. As an application of these results, we answer several conjectures on the connection between cluster algebras and quiver representations.

Affiliated with

Also associated with

No associations

Rating

Quivers with relations and cluster tilted algebras 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 Quivers with relations and cluster tilted algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quivers with relations and cluster tilted algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-480493