arXiv Analytics

Sign in

arXiv:2005.05536 [math.RT]AbstractReferencesReviewsResources

Rigid modules and ICE-closed subcategories over path algebras

Haruhisa Enomoto

Published 2020-05-12Version 1

We introduce image-cokernel-extension-closed (ICE-closed) subcategories of module categories. This class unifies both torsion classes and wide subcategories. We show that ICE-closed subcategories over the path algebra of Dynkin type are in bijection with basic rigid modules, and that the number does not depend on the orientation of the quiver. We give an explicit formula of this number for each Dynkin type, and in particular, it is equal to the large Schr\"oder number for type A case.

Comments: 15 pages, comments welcome
Categories: math.RT, math.RA
Subjects: 16G20, 16G10
Related articles: Most relevant | Search more
arXiv:2307.11347 [math.RT] (Published 2023-07-21)
Classifying $t$-structures via ICE-closed subcategories and a lattice of torsion classes
arXiv:1503.04639 [math.RT] (Published 2015-03-16)
Torsion classes, wide subcategories and localisations
arXiv:2102.08527 [math.RT] (Published 2021-02-17)
An introduction to the lattice of torsion classes

Links

Toolbox