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Steffen Oppermann

  1. The Gorenstein defect category.

    Ср, 02/15/2012 - 15:01 — SomNambul
    Authors: Steffen Oppermann, Petter Andreas Bergh, David A. Jorgensen
    Subjects: Category Theory
    Abstract

    We consider the homotopy category of complexes of projective modules over a
    Noetherian ring. Truncation at degree zero induces a fully faithful triangle
    functor from the totally acyclic complexes to the stable derived category. We
    show that if the ring is either Artin or commutative Noetherian local, then the
    functor is dense if and only if the ring is Gorenstein. Motivated by this, we
    define the Gorenstein defect category of the ring, a category which in some
    sense measures how far the ring is from being Gorenstein.

  2. The image of the derived category in the cluster category.

    Чт, 10/07/2010 - 15:01 — SomNambul
    Authors: Steffen Oppermann, Claire Amiot
    Subjects: Representation Theory
    Abstract

    Cluster categories of hereditary algebras have been introduced as orbit
    categories of their derived categories. Keller has pointed out that for
    non-hereditary algebras orbit categories need not be triangulated, and he
    introduced the notion of triangulated hull to overcome this problem. In this
    paper we study the image if the natural functor from the bounded derived
    category to the cluster category, that is we investigate how far the orbit
    category is from being the cluster category.

  3. Higher dimensional cluster combinatorics and representation theory.

    Пнд, 02/01/2010 - 16:01 — SomNambul
    Authors: Steffen Oppermann, Hugh Thomas
    Subjects: Representation Theory
    Abstract

    Higher Auslander algebras were introduced by Iyama generalizing classical
    concepts from representation theory of finite dimensional algebras. Recently
    these higher analogues of classical representation theory have been
    increasingly studied. Cyclic polytopes are classical objects of study in convex
    geometry. In particular, their triangulations have been studied with a view
    towards generalizing the rich combinatorial structure of triangulations of
    polygons. In this paper, we demonstrate a connection between these two
    seemingly unrelated subjects.

  4. Constructing tilted algebras from cluster-tilted algebras.

    Чт, 12/17/2009 - 16:01 — SomNambul
    Authors: Steffen Oppermann, Marco Angel Bertani-Økland, Anette Wrålsen
    Subjects: Representation Theory
    Abstract

    Any cluster-tilted algebra is the relation extension of a tilted algebra. We
    present a method to, given the distribution of a cluster-tilting object in the
    Auslander-Reiten quiver of the cluster category, construct all tilted algebras
    whose relation extension is the endomorphism ring of this cluster-tilting
    object.

  5. Finding a cluster-tilting object for a representation finite cluster-tilted algebra.

    Ср, 12/16/2009 - 16:01 — SomNambul
    Authors: Steffen Oppermann, Marco Angel Bertani-Økland, Anette Wrålsen
    Subjects: Representation Theory
    Abstract

    We provide a technique to find a cluster-tilting object having a given
    cluster-tilted algebra as endomorphism ring in the finite type case.

  6. n-representation-finite algebras and n-APR tilting.

    Пт, 09/04/2009 - 12:10 — SomNambul
    Authors: Osamu Iyama, Steffen Oppermann
    Subjects: Representation Theory
    Abstract

    We introduce the notion of n-representation-finiteness, generalizing
    representation-finite hereditary algebras. We establish the procedure of n-APR
    tilting, and show that it preserves n-representation-finiteness. We give some
    combinatorial description of this procedure, and use this to completely
    describe a class of n-representation-finite algebras called ``type A''.

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