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- Title
Tilting and Cluster Tilting for Preprojective Algebras and Coxeter Groups.
- Authors
Kimura, Yuta
- Abstract
We study the stable category of the graded Cohen–Macaulay modules of the factor algebra of the preprojective algebra associated with an element w of the Coxeter group of a quiver. We show that there exists a silting object M(w)| of this category associated with each reduced expression w of w and give a sufficient condition on w such that M(w) is a tilting object. In particular, the stable category is triangle equivalent to the derived category of the endomorphism algebra of M(w). Moreover, we compare it with a triangle equivalence given by Amiot–Reiten–Todorov for a cluster category.
- Subjects
GROUP algebras; COXETER groups; FACTORS (Algebra); MODULES (Algebra); CLUSTER algebras; ENDOMORPHISMS; ALGEBRA
- Publication
IMRN: International Mathematics Research Notices, 2019, Vol 2019, Issue 18, p5597
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnx265