Category theory for conformal boundary conditions

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dc.creatorFuchs, J.
dc.creatorSchweigert, C.
dc.date2001-06-07
dc.date2006-08-04
dc.date.accessioned2026-07-07T06:35:25Z
dc.date.available2026-07-07T06:35:25Z
dc.descriptionWe study properties of the category of modules of an algebra object A in a tensor category C. We show that the module category inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As a by-product we obtain results about the Frobenius-Schur indicator in sovereign tensor categories. A braiding on C is not needed, nor is semisimplicity. We apply our results to the description of boundary conditions in two-dimensional conformal field theory and present illustrative examples. We show that when the module category is tensor, then it gives rise to a NIM-rep of the fusion rules, and discuss a possible relation with the representation theory of vertex operator algebras.
dc.description47 pages, LaTeX2e + epsf + fic-l style; v2: More concise conjectures in section 6, with more comments on torus and annulus partition functions, and on NIM-reps in section 7; v3: Dropped assumption of semisimplicity in former lemma 5.24; lemma moved to section 4, is now lemma 4.15; v4: corrected part (ii) of proof of proposition 5.1
dc.identifierhttps://arxiv.org/abs/math/0106050
dc.identifierhttp://arxiv.org/abs/math/0106050
dc.identifierFields Institute Communications 39 (2003) 25-71
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99785
dc.subjectCategory Theory
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.subject17B69, 18D10, 81R10, 14H60
dc.titleCategory theory for conformal boundary conditions
dc.typetext

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