Grothendieck groups and tilting objects
表示论
2007-05-23 v1
摘要
Let C be a connected noetherian hereditary abelian Ext-finite category with Serre functor over an algebraically closed field k, with finite dimensional homomorphism and extension spaces. Using the classification of such categories from math.RT/9911242, we prove that if C has some object of infinite length, then the Grothendieck group of C is finitely generated if and only if C has a tilting object.
引用
@article{arxiv.math/0005100,
title = {Grothendieck groups and tilting objects},
author = {I. Reiten and M. Van den Bergh},
journal= {arXiv preprint arXiv:math/0005100},
year = {2007}
}