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Mathematics > Quantum Algebra

arXiv:1807.00415 (math)
[Submitted on 1 Jul 2018]

Title:Fusion categories for affine vertex algebras at admissible levels

Authors:Thomas Creutzig
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Abstract:The main result is that the category of ordinary modules of an affine vertex operator algebra of a simply laced Lie algebra at admissible level is rigid and thus a braided fusion category. If the level satisfies a certain coprime property then it is even a modular tensor category. In all cases open Hopf links coincide with the corresponding normalized S-matrix entries of torus one-point functions. This is interpreted as a Verlinde formula beyond rational vertex operator algebras.
A preparatory Theorem is a convenient formula for the fusion rules of rational principal W-algebras of any type.
Subjects: Quantum Algebra (math.QA); Category Theory (math.CT); Representation Theory (math.RT)
Cite as: arXiv:1807.00415 [math.QA]
  (or arXiv:1807.00415v1 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.1807.00415

Submission history

From: Thomas Creutzig [view email]
[v1] Sun, 1 Jul 2018 23:29:02 UTC (17 KB)
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