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Realising higher cluster categories of Dynkin type as stable module categories

Lookup NU author(s): Professor Peter Jorgensen

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Abstract

We show that the stable module categories of certain self-injective algebras of finite representation type having tree class An, Dn, E6, E7 or E8 are triangulated equivalent to u-cluster categories of the corresponding Dynkin type. The proof relies on the ‘Morita’ theorem for u-cluster categories by Keller and Reiten, along with the recent computation of Calabi–Yau dimensions of stable module categories by Dugas.

Publication metadata

Author(s): Holm T, Jorgensen P

Publication type: Article

Publication status: Published

Journal: Quarterly Journal of Mathematics

Year: 2013

Volume: 64

Issue: 2

Pages: 409-435

Print publication date: 01/06/2013

Online publication date: 03/05/2012

ISSN (print): 0033-5606

ISSN (electronic): 1464-3847

Publisher: Oxford University Press

URL: http://dx.doi.org/10.1093/qmath/has013

DOI: 10.1093/qmath/has013

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