Symplectic fermions and a quasi-Hopf algebra structure on U‾isℓ(2)

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Autor/in:
Erscheinungsjahr:
2017
Medientyp:
Text
Schlagworte:
  • Hopf algebra
  • Category
  • Fusion category
  • Algebra
  • Module
  • Conformal field theory
  • Quasi-Hopf algebras
  • Non-semisimple braided tensor categories
  • Modular group action
  • Quantum groups
  • Hopf algebra
  • Category
  • Fusion category
  • Algebra
  • Module
Beschreibung:
  • We consider the (finite-dimensional) restricted quantum group U‾qsℓ(2) at q=i. We show that U‾isℓ(2) does not allow for a universal R-matrix, even though U⊗V≅V⊗U holds for all finite-dimensional representations U,V of U‾isℓ(2). We then give an explicit coassociator Φ and a universal R-matrix R such that U‾isℓ(2) becomes a quasi-triangular quasi-Hopf algebra. Our construction is motivated by the two-dimensional chiral conformal field theory of symplectic fermions with central charge c=−2. There, a braided monoidal category, SF, has been computed from the factorisation and monodromy properties of conformal blocks, and we prove that Rep(U‾isℓ(2),Φ,R) is braided monoidally equivalent to SF.
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  • info:eu-repo/semantics/restrictedAccess
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Forschungsinformationssystem der UHH

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oai:www.edit.fis.uni-hamburg.de:publications/20130043-ac86-493f-af5a-f6a7b7af164b