The Nichols algebra of screenings

Abstract

Two related constructions are associated with screening operators in models of two-dimensional conformal field theory. One is a local system constructed in terms of the braided vector space X spanned by the screening species in a given CFT model and the space of vertex operators Y and the other is the Nichols algebra B(X) and the category of its Yetter--Drinfeld modules, which we propose as an algebraic counterpart, in a "braided" version of the Kazhdan--Lusztig duality, of the representation category of vertex-operator algebras realized in logarithmic CFT models.

V3: now only 63 pages (with hopefully increased readability). LaTeX: amsmath++, mathabx, times, xy

References in corpus (24)

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• Associative-algebraic approach to logarithmic conformal field theories
• Kazhdan--Lusztig-dual quantum group for logarithmic extensions of Virasoro minimal models
• Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras
• From boundary to bulk in logarithmic CFT
• The Triplet Vertex Operator Algebra W(p) and the Restricted Quantum Group at Root of Unity
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• Logarithmic tensor category theory, VI: Expansion condition, associativity of logarithmic intertwining operators, and the associativity isomorphisms
• The logarithmic triplet theory with boundary
• The N=1 triplet vertex operator superalgebras
• Logarithmic tensor category theory, V: Convergence condition for intertwining maps and the corresponding compatibility condition
• Nichols algebras of group type with many quadratic relations
• Logarithmic tensor category theory, III: Intertwining maps and tensor product bifunctors
• Logarithmic tensor category theory, IV: Constructions of tensor product bifunctors and the compatibility conditions
• A modular invariant bulk theory for the c=0 triplet model
• Lusztig limit of quantum sl(2) at root of unity and fusion of (1,p) Virasoro logarithmic minimal models
• Kazhdan-Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models
• Factorizable ribbon quantum groups in logarithmic conformal field theories
• Some remarks on Nichols algebras
• Categorical centers and Reshetikhin-Turaev invariants
• The structure of Zhu's algebras for certain W-algebras
• Logarithmic tensor category theory for generalized modules for a conformal vertex algebra, I: Introduction and strongly graded algebras and their generalized modules
• Hopf algebras and finite tensor categories in conformal field theory
• Nichols algebras of unidentified diagonal type

Cited by in corpus (19)

• Lattice fusion rules and logarithmic operator product expansions
• A quasi-Hopf algebra for the triplet vertex operator algebra
• Kazhdan-Lusztig equivalence and fusion of Kac modules in Virasoro logarithmic models
• A classification of Nichols algebras of semi-simple Yetter-Drinfeld modules over non-abelian groups
• Modular invariant Frobenius algebras from ribbon Hopf algebra automorphisms
• Logarithmic ^sl(2) CFT models from Nichols algebras. 1
• The classification of Nichols algebras over groups with finite root system of rank two
• Logarithmic conformal field theories of type $B_n,\ell =4$ and symplectic fermions
• Rank 2 Nichols Algebras of Diagonal Type over Fields of Positive Characteristic
• The Cardy-Cartan modular invariant
• BCJ, worldsheet quantum algebra and KZ equations
• Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra
• The R-matrix of quantum doubles of Nichols algebras of diagonal type
• Representations of ${\bar{U}}_{q}s\ell (2|1)$ at even roots of unity
• Integrable perturbations of conformal field theories and Yetter-Drinfeld modules
• Nichols Algebras and Quantum Principal Bundles
• A note on the "logarithmic-W_3" octuplet algebra and its Nichols algebra
• Quasi-lisse extension of affine ${\mathfrak{sl}}_2$ à la Feigin--Tipunin
• Bimodule structure of the mixed tensor product over $U_{q}s\ell (2|1)$ and quantum walled Brauer algebra