Cluster structures for 2-Calabi-Yau categories and unipotent groups

Details Cluster structures for 2-Calabi-Yau categories and unipotent groups Cluster structures for 2-Calabi-Yau categories and unipotent groups

2007-01-19

arxiv.org/abs/math/0701557v3

Mathematics

Representation Theory

49 pages. For the third version the presentation is revised, especially Chapter III replaces the old Chapter III and IV

Scientific paper

We investigate cluster tilting objects (and subcategories) in triangulated 2-Calabi-Yau categories and related categories. In particular we construct a new class of such categories related to preprojective algebras of non Dynkin quivers associated with elements in the Coxeter group. This class of 2-Calabi-Yau categories contains the cluster categories and the stable categories of preprojective algebras of Dynkin graphs as special cases. For these 2-Calabi-Yau categories we construct cluster tilting objects associated with each reduced expression. The associated quiver is described in terms of the reduced expression. Motivated by the theory of cluster algebras, we formulate the notions of (weak) cluster structure and substructure, and give several illustrations of these concepts. We give applications to cluster algebras and subcluster algebras related to unipotent groups, both in the Dynkin and non Dynkin case.

Affiliated with

Also associated with

No associations

Rating

Cluster structures for 2-Calabi-Yau categories and unipotent groups 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 Cluster structures for 2-Calabi-Yau categories and unipotent groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cluster structures for 2-Calabi-Yau categories and unipotent groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-651932