Affiliation:
1. Département de Mathématiques , LACIM, Université du Québec à Montréal and Département de Mathématiques, Université de Sherbrooke
Abstract
Abstract
We generalize the “facial weak order” of a finite Coxeter group to a partial order on a set of intervals in a complete lattice. We apply our construction to the lattice of torsion classes of a finite-dimensional algebra and consider its restriction to intervals coming from stability conditions. We give two additional interpretations of the resulting “facial semistable order”: one using cover relations, and one using Bongartz completions of 2-term presilting objects. For $\tau $-tilting finite algebras, this allows us to prove that the facial semistable order is a semidistributive lattice. We then show that, in any abelian length category, our new partial order can be partitioned into a set of completely semidistributive lattices, one of which is the original lattice of torsion classes.
Funder
Canada Research Chairs program
Natural Sciences and Engineering Research Council of Canada
Publisher
Oxford University Press (OUP)
Reference57 articles.
1. Cluster Configuration Spaces of Finite Type
2. Fans and polytopes in tilting theory I: foundations.”;Aoki
3. Semistable torsion classes and canonical decompositions in Grothendieck groups.”;Asai
4. tilting theory;Adachi;Compos. Math.,2014
5. Classes of Semidistributive Lattices
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Correction to: A Facial Order for Torsion Classes;International Mathematics Research Notices;2024-09-03