Correspondences of ribbon categories
type: Item
instance of: scholarly article
title: Correspondences of ribbon categories
zbMATH Open document ID: 1087.18006
author: Jürgen Fuchs
author: Ingo Runkel
author: Christoph Schweigert
author: Jürg Fröhlich
published in: Advances in Mathematics
publication date: 2005-12-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0309465
review text: In this lengthy paper, algebras and their modules internal to a braided tensor category \(\mathcal{C}\) are studied in depth. Most of the theory depends vitally on the braiding not being a symmetry. The left and right centres of a Frobenius algebra \(A\) in \(\mathcal{C}\) are defined and found to have equivalent categories of dyslectic modules in the sense of \textit{B. Pareigis} [``On braiding and dyslexia'', J. Algebra 171, 413--425 (1995; Zbl 0816.18003)]. This is applied to the classification of modular invariants and the construction of two-dimensional conformal field theories. Another result proved here is that, for each modular category \(\mathcal{C}\), there exists a commutative Frobenius algebra \(A\) in a certain semidirect product of \(\mathcal{C}\) and \(\mathcal{C}^{\mathrm{op}}\) such that the category of dyslectic \(A\)-modules is equivalent to the category of vector spaces. This is applied to the study of ``correspondences'' of braided tensor categories.
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 81T40
zbMATH DE Number: 2242282
zbMATH Keywords: modular categories
zbMATH Keywords: ribbon categories
zbMATH Keywords: tortile monoidal categories
zbMATH Keywords: quantum field theory
zbMATH Keywords: local modules
zbMATH Keywords: coset models
reviewed by: Ross H. Street
MaRDI profile type: Publication
OpenAlex ID: W2101546965
arXiv ID: math/0309465
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DOI: 10.1016/J.AIM.2005.04.007
description: scientific article