Christoph Schweigert
Modular categories from finite crossed modules.
Thu, 03/11/2010 - 16:01 — SomNambulAuthors: Christoph Schweigert, Jennifer Maier
Subjects: Quantum Algebra
AbstractIt is known that finite crossed modules provide premodular tensor categories.
These categories are in fact modularizable. We construct the modularization and
show that it is equivalent to the module category of a finite Drinfeld double.On the Rosenberg-Zelinsky sequence in abelian monoidal categories.
Thu, 12/10/2009 - 16:01 — SomNambulAuthors: Ingo Runkel, Christoph Schweigert, Till Barmeier, J"urgen Fuchs
Subjects: Category Theory
AbstractWe 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.Defect lines, dualities, and generalised orbifolds.
Tue, 09/29/2009 - 15:21 — SomNambulAuthors: Ingo Runkel, Jürg Fröhlich, Jürgen Fuchs, Christoph Schweigert
Subjects: Mathematical Physics
AbstractDefects 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.
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