Grothendieck groups and tilting objects

Details Grothendieck groups and tilting objects Grothendieck groups and tilting objects

2000-05-10

arxiv.org/abs/math/0005100v1

Mathematics

Representation Theory

Scientific paper

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.

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