The Ziegler spectrum for derived-discrete algebras

Kristin Krogh Arnesen, Rosanna Laking, David Pauksztello, Michael Prest

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Let be a derived-discrete algebra. We show that the Krull-Gabriel dimension
    of the homotopy category of projective -modules, and therefore the Cantor-
    Bendixson rank of its Ziegler spectrum, is 2, thus extending a result of Bobinski and Krause [8]. We also describe all the indecomposable pure-injective complexes and hence the Ziegler spectrum for derived-discrete algebras, extending a result of Z. Han [17]. Using this, we are able to prove that all indecomposable complexes in the homotopy category of projective -modules are pure-injective, so obtaining a class of algebras for which every indecomposable complex is pure-injective but which are not derived pure-semisimple.
    Original languageEnglish
    Pages (from-to)653-698
    JournalAdvances in Mathematics
    Volume319
    Issue number0
    DOIs
    Publication statusPublished - 11 Sept 2017

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