383 citations · 818 across the 19 of their papers we have counts for
20 papers
A manifestly Morita-invariant construction of Turaev-Viro invariants
Jürgen Fuchs, César Galindo, David Jaklitsch +1
We present a state sum construction that assigns a scalar to a skeleton in a closed oriented three-dimensional manifold. The input datum is the pivotal bicategory $\mathbf{Mod}^{\m…
A Graded Schur Lemma and a graded-monoidal structure for induced modules over graded-commutative algebras
Jürgen Fuchs, Tobias Grøsfjeld
We consider algebras and Frobenius algebras, internal to a monoidal category, that are graded over a finite abelian group. For the case that A is a twisted group algebra in a linea…
String-net models for pivotal bicategories
Jürgen Fuchs, Christoph Schweigert, Yang Yang
We develop a string-net construction of a modular functor whose algebraic input is a pivotal bicategory; this extends the standard construction based on a spherical fusion category…
Spherical Morita contexts and relative Serre functors
Jürgen Fuchs, César Galindo, David Jaklitsch +1
The Morita context provided by an exact module category over a finite tensor category gives a two-object bicategory with duals. Right and left duals of objects in the module catego…
Module Eilenberg-Watts calculus
Jürgen Fuchs, Gregor Schaumann, Christoph Schweigert
The categorical formulation of the Eilenberg-Watts calculus relates, for any pair of finite categories M and N, the finite categories Fun^{le}(N,M) and Fun^{re}(N,M) of linear left…
A modular functor from state sums for finite tensor categories and their bimodules
Jürgen Fuchs, Gregor Schaumann, Christoph Schweigert
We construct a modular functor which takes its values in the monoidal bicategory of finite categories, left exact functors and natural transformations. The modular functor is defin…
Eilenberg-Watts calculus for finite categories and a bimodule Radford theorem
Jürgen Fuchs, Gregor Schaumann, Christoph Schweigert
We obtain Morita invariant versions of Eilenberg-Watts type theorems, relating Deligne products of finite linear categories to categories of left exact as well as of right exact fu…
On the Killing form of Lie Algebras in Symmetric Ribbon Categories
Igor Buchberger, Jürgen Fuchs
As a step towards the structure theory of Lie algebras in symmetric monoidal categories we establish results involving the Killing form. The proper categorical setting for discussi…
Modular invariant Frobenius algebras from ribbon Hopf algebra automorphisms
Jurgen Fuchs, Christoph Schweigert, Carl Stigner
For any finite-dimensional factorizable ribbon Hopf algebra H and any ribbon automorphism omega of H, we establish the existence of the following structure: an H-bimodule F_omega a…
The classifying algebra for defects
Jurgen Fuchs, Christoph Schweigert, Carl Stigner
We demonstrate that topological defects in a rational conformal field theory can be described by a classifying algebra for defects - a finite-dimensional semisimple unital commutat…
Hopf algebras and finite tensor categories in conformal field theory
Jurgen Fuchs, Christoph Schweigert
In conformal field theory the understanding of correlation functions can be divided into two distinct conceptual levels: The analytic properties of the correlators endow the repres…
Hopf algebras and Frobenius algebras in finite tensor categories
Christoph Schweigert, Jürgen Fuchs
We discuss algebraic and representation theoretic structures in braided tensor categories C which obey certain finiteness conditions. Much interesting structure of such a category…
Twenty-five years of two-dimensional rational conformal field theory
Jürgen Fuchs, Ingo Runkel, Christoph Schweigert
In this article we try to give a condensed panoramic view of the development of two-dimensional rational conformal field theory in the last twenty-five years.
Defect lines, dualities, and generalised orbifolds
Jürg Fröhlich, Jürgen Fuchs, Ingo Runkel +1
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 t…
Module categories for permutation modular invariants
Till Barmeier, Jurgen Fuchs, Ingo Runkel +1
We show that a braided monoidal category C can be endowed with the structure of a right (and left) module category over C \times C. In fact, there is a family of such module catego…
Algebras in tensor categories and coset conformal field theories
J"urg Fr"ohlich, J"urgen Fuchs, Ingo Runkel +1
The coset construction is the most important tool to construct rational conformal field theories with known chiral data. For some cosets at small level, so-called maverick cosets,…
Nonsemisimple Fusion Algebras and the Verlinde Formula
J. Fuchs, S. Hwang, A. M. Semikhatov +1
We find a nonsemisimple fusion algebra F_p associated with each (1,p) Virasoro model. We present a nonsemisimple generalization of the Verlinde formula which allows us to derive F_…
TFT construction of RCFT correlators I: Partition functions
Jürgen Fuchs, Ingo Runkel, Christoph Schweigert
We formulate rational conformal field theory in terms of a symmetric special Frobenius algebra A and its representations. A is an algebra in the modular tensor category of Moore-Se…
Lectures on conformal field theory and Kac-Moody algebras
J. Fuchs
This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.
Modular invariants and fusion rule automorphisms from Galois theory
Jürgen Fuchs, Beatriz Gato-Rivera, Bert Schellekens +1
We show that Galois theory of cyclotomic number fields provides a powerful tool to construct systematically integer-valued matrices commuting with the modular matrix S, as well as…