Correspondences of ribbon categories

Details Correspondences of ribbon categories Correspondences of ribbon categories

2003-09-29

arxiv.org/abs/math/0309465v3

Adv.Math.199:192-329,2006

Mathematics

Category Theory

129 pages; several figures. v2: remark 7.4(ii) corrected, conditions in theorem 7.6 and in corollary 7.7 adapted. v3 (version

Scientific paper

10.1016/j.aim.2005.04.007

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.

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