2006/12/15 by Thorsten Holm, Holm, Thorsten, Peter Jorgensen +1
Mathematics · #05E99 #16D50 #16G10 #16G60 #16G70 (Secondary) #18E30 (Primary) #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:05E99 #msc:16D50 #msc:16G10 #msc:16G60 #msc:16G70 #msc:18E30
paper · pdf · doi:10.48550/arxiv.math/0612451
This preprint has been withdrawn
arxiv created 2010/02/19 · arxiv updated 2010/02/26
The preprints arXiv:math/0610728 and arXiv:math/0612451 are withdrawn due to a problem with Theorem 2.2 in arXiv:math/0610728. The theorem claims that for certain triangulated categories with finitely many indecomposable objects, the Calabi-Yau dimension can be computed combinatorially, by finding the smallest d for which the Serre functor and the d'th power of the suspension functor have the same action on the Auslander-Reiten quiver. This is false, and we are grateful to Alex Dugas for pointing out a counterexample; see Section 5 of his paper arXiv:math/0808.1311 for more details. Unfortunately, we are not presently able to come up with a corrected version of the theorem, and this means that we cannot compute the Calabi-Yau dimensions of concrete stable module categories. Since these dimensions are necessary for identifying the categories with higher cluster categories, we presently have no means to achieve such identifications.