2016/03/02 by Kristin Krogh Arnesen, Rosanna Laking, Arnesen, Kristin Krogh +5
Mathematics · #16G10 #18E30 #18E35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1603.00775
openalex publication_date 2016/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Λ be a derived-discrete algebra. We show that the Krull-Gabriel dimension of the homotopy category of projective Λ-modules, and therefore the Cantor-Bendixson rank of its Ziegler spectrum, is 2, thus extending a result of Bobiński and Krause. We also describe all the indecomposable pure-injective complexes and hence the Ziegler spectrum for derived-discrete algebras, extending a result of Z. Han. Using this, we are able to prove that all indecomposable complexes in the homotopy category of projective Λ-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.