Correspondences of ribbon categories

• DOI: 10.1016/j.aim.2005.04.007
• Publication Date: 2005-06-15T11:43:59Z
• Authors: Jürg Fröhlich; Jürgen Fuchs; Ingo Runkel; Christoph Schweigert
• Keywords: High Energy Physics - Theory; Mathematics(all); FOS: Physical sciences; Ribbon categories; Mathematics - Category Theory; 01 natural sciences; Modular categories; Coset models; High Energy Physics - Theory (hep-th); Local modules; 0103 physical sciences; FOS: Mathematics; Category Theory (math.CT); 0101 mathematics

Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories. Several results are established that do not have a substantial counterpart for symmetric tensor categories. In particular, we exhibit various equivalences involving categories of modules over algebras in ribbon categories. Finally we establish a correspondence of ribbon categories that can be applied to, and is in fact motivated by, the coset construction in conformal quantum field theory.<br/>129 pages; several figures. v2: remark 7.4(ii) corrected, conditions in theorem 7.6 and in corollary 7.7 adapted. v3 (version to appear in Adv.Math.): typos corrected<br/>