Главная

Ingo Runkel

  1. On the Rosenberg-Zelinsky sequence in abelian monoidal categories.

    Чт, 12/10/2009 - 16:01 — SomNambul
    Authors: Ingo Runkel, Christoph Schweigert, Till Barmeier, J"urgen Fuchs
    Subjects: Category Theory
    Abstract

    We consider Frobenius algebras and their bimodules in certain abelian
    monoidal categories. In particular we study the Picard group of the category of
    bimodules over a Frobenius algebra, i.e. the group of isomorphism classes of
    invertible bimodules. The Rosenberg-Zelinsky sequence describes a homomorphism
    from the group of algebra automorphisms to the Picard group, which however is
    typically not surjective. We investigate under which conditions there exists a
    Morita equivalent Frobenius algebra for which the corresponding homomorphism is
    surjective.

  2. Defect lines, dualities, and generalised orbifolds.

    Втр, 09/29/2009 - 15:21 — SomNambul
    Authors: Ingo Runkel, Jürg Fröhlich, Jürgen Fuchs, Christoph Schweigert
    Subjects: Mathematical Physics
    Abstract

    Defects are a useful tool in the study of quantum field theories. This is
    illustrated in the example of two-dimensional conformal field theories. We
    describe how defect lines and their junction points appear in the description
    of symmetries and order-disorder dualities, as well as in the orbifold
    construction and a generalisation thereof that covers exceptional modular
    invariants.

  3. On the monoidal structure of matrix bi-factorisations.

    Сб, 09/26/2009 - 04:10 — SomNambul
    Authors: Ingo Runkel, Nils Carqueville
    Subjects: Mathematical Physics
    Abstract

    We investigate tensor products of matrix factorisations. This is most
    naturally done by formulating matrix factorisations in terms of bimodules
    instead of modules. If the underlying ring is C[x_1,...,x_N] we show that
    bimodule matrix factorisations form a monoidal category.

  4. Affine su(2) fusion rules from gerbe 2-isomorphisms.

    Чт, 09/03/2009 - 17:38 — SomNambul
    Authors: Ingo Runkel, Rafal R. Suszek
    Subjects: Differential Geometry
    Abstract

    We give a geometric description of the fusion rules of the affine Lie algebra
    su(2)_k at a positive integer level k in terms of the k-th power of the basic
    gerbe over the Lie group SU(2). The gerbe can be trivialised over conjugacy
    classes corresponding to dominant weights of su(2)_k via a 1-isomorphism. The
    fusion-rule coefficients are related to the existence of a 2-isomorphism
    between pullbacks of these 1-isomorphisms to a submanifold of SU(2) x SU(2)
    determined by the corresponding three conjugacy classes.

  5. Affine su(2) fusion rules from gerbe 2-isomorphisms.

    Чт, 09/03/2009 - 17:38 — SomNambul
    Authors: Ingo Runkel, Rafal R. Suszek
    Subjects: Differential Geometry
    Abstract

    We give a geometric description of the fusion rules of the affine Lie algebra
    su(2)_k at a positive integer level k in terms of the k-th power of the basic
    gerbe over the Lie group SU(2). The gerbe can be trivialised over conjugacy
    classes corresponding to dominant weights of su(2)_k via a 1-isomorphism. The
    fusion-rule coefficients are related to the existence of a 2-isomorphism
    between pullbacks of these 1-isomorphisms to a submanifold of SU(2) x SU(2)
    determined by the corresponding three conjugacy classes.

Math-arch

RSS-материал