More finite sets coming from non-commutative counting
Abstract
In our previous papers we introduced categorical invariants, which are, roughly speaking, sets of triangulated subcategories in a given triangulated category and their quotients. Here is extended the list of examples, where these sets are finite. Using results by Geigle, Lenzning, Meltzer, H\"ubner for weighted projective lines we show that for any two affine acyclic quivers , (i.e. quivers of extended Dynkin type) there are only finitely many full triangulated subctegories in , which are equivalent to , where is an algebraically closed field. Some of the numbers counting the elements in these finite sets are explicitly determined.
Cite
@article{arxiv.1903.00295,
title = {More finite sets coming from non-commutative counting},
author = {George Dimitrov and Ludmil Katzarkov},
journal= {arXiv preprint arXiv:1903.00295},
year = {2019}
}
Comments
16 pages, In v3 Corollary 5.6 does not depend on any additional conditions, because in a private communication Professor Helmut Lenzing confirmed that (21) is correct. The last section 6 and the introduction in the new version are slightly extended. The reference list is also updated