Grothendieck Groups and Tilting Objects |
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| Authors: | Idun Reiten Michel Van den Bergh |
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| Affiliation: | (1) Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway;(2) Department WNI, Limburgs Universitair Centrum, Universitaire Campus, Building D, 3590 Diepenbeek, Belgium |
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| Abstract: | Let C be a connected Noetherian hereditary Abelian category with a Serre functor over an algebraically closed field k, with finite-dimensional homomorphism and extension spaces. Using the classification of such categories from our 1999 preprint, 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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| Keywords: | Grothendieck group tilting object hereditary Abelian category hereditary order quotient category |
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