The Triplet Vertex Operator Algebra W(p) and the Restricted Quantum Group at Root of Unity

Abstract

We prove the abelian category of the modules over triplet VOA W(p) is category equivalent to the abelian category of the modules over quantum algebra of type sl_2 at root of unity.

48 pages

References in corpus (7)

• Vertex Algebras and Algebraic Curves
• Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center
• Logarithmic Minimal Models
• Logarithmic extensions of minimal models: characters and modular transformations
• Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras
• On the triplet vertex algebra W(p)
• Classification of irreducible modules of certain subalgebras of free boson vertex algebra

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• Symplectic fermions and a quasi-Hopf algebra structure on ${\bar{U}}_{i}sl(2)$
• The Nichols algebra of screenings
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• Indecomposable decomposition of tensor products of modules over the restricted quantum universal enveloping algebra associated to ${\mathfrak{sl}}_2$
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• Critical dense polymers with Robin boundary conditions, half-integer Kac labels and ${\mathbb{Z}}_4$ fermions
• Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra
• On the Feigin-Tipunin conjecture
• Ambidextrous objects and trace functions for nonsemisimple categories
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• On Regularised Quantum Dimensions of the Singlet Vertex Operator Algebra and False Theta Functions
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• A Heisenberg double addition to the logarithmic Kazhdan--Lusztig duality
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• Simplicity of higher rank triplet W-algebras
• Some remarks on pseudo-trace functions for orbifold models associated with symplectic fermions
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• A note on the "logarithmic-W_3" octuplet algebra and its Nichols algebra
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• ADE subalgebras of the triplet vertex algebra W(p): A-series
• Hopf and Frobenius algebras in conformal field theory
• The quantum group dual of the first-row subcategory for the generic Virasoro VOA
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• The unrolled quantum group inside Lusztig's quantum group of divided powers