A+ CATEGORY SCIENTIFIC UNIT

Endomorphism rings of maximal rigid objects in cluster tubes

Volume 123 / 2011

Dagfinn F. Vatne Colloquium Mathematicum 123 (2011), 63-93 MSC: 16G20, 18E30. DOI: 10.4064/cm123-1-6

Abstract

We describe the endomorphism rings of maximal rigid objects in the cluster categories of tubes. Moreover, we show that they are gentle and have Gorenstein dimension 1. We analyse their representation theory and prove that they are of finite type. Finally, we study the relationship between the module category and the cluster tube via the Hom-functor.

Authors

  • Dagfinn F. VatneInstitutt for Matematiske Fag
    Norges Teknisk-Naturvitenskapelige Universitet
    N-7491 Trondheim, Norway
    e-mail

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