Home > Research > Publications & Outputs > Functorially finite hearts, simple-minded syste...

Electronic data


Text available via DOI:

View graph of relations

Functorially finite hearts, simple-minded systems in negative cluster categories, and noncrossing partitions

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>31/01/2022
<mark>Journal</mark>Compositio Mathematica
Issue number1
Number of pages33
Pages (from-to)211-243
Publication StatusPublished
<mark>Original language</mark>English


Let Q be an acyclic quiver and w⩾1 be an integer. Let C−w(kQ) be the (−w)-cluster category of kQ. We show that there is a bijection between simple-minded collections in Db(kQ) lying in a fundamental domain of C−w(kQ) and w-simple-minded systems in C−w(kQ). This generalises the same result of Iyama–Jin in the case that Q is Dynkin. A key step in our proof is the observation that the heart H of a bounded t-structure in a Hom-finite, Krull–Schmidt, k-linear saturated triangulated category D is functorially finite in D if and only if H has enough injectives and enough projectives. We then establish a bijection between w-simple-minded systems in C−w(kQ) and positive w-noncrossing partitions of the corresponding Weyl group WQ.

Bibliographic note

http://journals.cambridge.org/action/displayJournal?jid=UHY The final, definitive version of this article has been published in the Journal, Compositio Mathematica, 158 (1), pp 211-243 2022, © 2022 Cambridge University Press.