Tensor categories of affine Lie algebras beyond admissible levels
From MaRDI portal
Publication:2049972
DOI10.1007/s00208-021-02159-wOpenAlexW3131049771MaRDI QIDQ2049972
Publication date: 27 August 2021
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2002.05686
Vertex operators; vertex operator algebras and related structures (17B69) Fusion categories, modular tensor categories, modular functors (18M20)
Related Items (15)
Correspondences of categories for subregular \(\mathcal{W}\)-algebras and principal \(\mathcal{W}\)-superalgebras ⋮ Direct limit completions of vertex tensor categories ⋮ On the semisimplicity of the category \(KL_k\) for affine Lie superalgebras ⋮ Uprolling unrolled quantum groups ⋮ Rigid tensor structure on big module categories for some \(W\)-(super)algebras in type \(A\) ⋮ Ribbon tensor structure on the full representation categories of the singlet vertex algebras ⋮ On the extensions of the left modules for a meromorphic open-string vertex algebra. I ⋮ Tensor Categories for Vertex Operator Superalgebra Extensions ⋮ Tensor category \(\mathrm{KL}_k (\mathfrak{sl}_{2n})\) via minimal affine \(W\)-algebras at the non-admissible level \(k = - \frac{2n + 1}{2}\) ⋮ Mini-workshop: Recent developments in representation theory and mathematical physics. Abstracts from the mini-workshop held March 20--26, 2022 ⋮ On ribbon categories for singlet vertex algebras ⋮ Trialities of orthosymplectic \(\mathcal{W} \)-algebras ⋮ Admissible-level \(\mathfrak{sl}_3\) minimal models ⋮ Urod algebras and Translation of W-algebras ⋮ On the representation theory of the vertex algebra L−5/2(sl(4))
Cites Work
- A realization of certain modules for the \(N = 4\) superconformal algebra and the affine Lie algebra \(a_{2}^{(1)}\)
- Rationality of \(W\)-algebras: principal nilpotent cases
- Extension of the category \({\mathcal O}^ g\) and a vanishing theorem for the Ext functor for Kac-Moody algebras
- Quantum reduction and representation theory of superconformal algebras
- On complete reducibility for infinite-dimensional Lie algebras
- Finite vs. infinite decompositions in conformal embeddings
- Braided tensor categories related to \(\mathcal{B}_p\) vertex algebras
- Representation theory of superconformal algebras and the Kac-Roan-Wakimoto conjecture
- Classical and quantum conformal field theory
- Vertex tensor category structure on a category of Kazhdan-Lusztig
- Cofiniteness conditions, projective covers and the logarithmic tensor product theory
- Infinite conformal symmetry in two-dimensional quantum field theory
- Current algebras and Wess-Zumino model in two dimensions
- Structure of representations with highest weight of infinite-dimensional Lie algebras
- Structure of some categories of representations of infinite-dimensional Lie algebras
- Vertex operator algebras associated to representations of affine and Virasoro algebras
- Vertex operator algebras and associative algebras
- Determining fusion rules by \(A(V)\)-modules and bimodules
- Quantum reduction for affine superalgebras
- Braided tensor categories of admissible modules for affine Lie algebras
- W-algebras for Argyres-Douglas theories
- Conformal embeddings of affine vertex algebras in minimal \(W\)-algebras. I: Structural results
- Logarithmic W-algebras and Argyres-Douglas theories at higher rank
- Fusion categories for affine vertex algebras at admissible levels
- Logarithmic link invariants of \(\overline{U}_q^H(\mathfrak{sl}_2)\) and asymptotic dimensions of singlet vertex algebras
- On a \(q\)-analogue of the McKay correspondence and the ADE classification of \(\mathfrak{sl}_{2}\) conformal field theories
- A theory of tensor products for module categories for a vertex operator algebra. III
- A theory of tensor products for module categories for a vertex operator algebra. IV
- A theory of tensor products for module categories for a vertex operator algebra. I
- A theory of tensor products for module categories for a vertex operator algebra. II
- Intertwining operator algebras and vertex tensor categories for affine Lie algebras
- S-duality for the large \(N = 4\) superconformal algebra
- On the tensor structure of modules for compact orbifold vertex operator algebras
- Vertex algebras for S-duality
- Tensor categories arising from the Virasoro algebra
- Conformal embeddings in affine vertex superalgebras
- Quantum Langlands dualities of boundary conditions, \(D\)-modules, and conformal blocks
- Schur-Weyl duality for Heisenberg cosets
- \(W\)-algebras as coset vertex algebras
- Braided tensor categories and extensions of vertex operator algebras
- Conformal embeddings of affine vertex algebras in minimal \(W\)-algebras. II: Decompositions
- Orbifolds and cosets of minimal \({\mathcal{W}}\)-algebras
- Sheets and associated varieties of affine vertex algebras
- Relaxed highest-weight modules. I: Rank 1 cases
- Relating the archetypes of logarithmic conformal field theory
- Modular data and Verlinde formulae for fractional level WZW models. II
- Representations of certain non-rational vertex operator algebras of affine type
- Space of unitary vector bundles on a compact Riemann surface
- The vertex algebras \(\mathcal{R}^{(p)}\) and \(\mathcal{V}^{(p)}\)
- Tensor Structures Arising from Affine Lie Algebras. I
- A LOGARITHMIC GENERALIZATION OF TENSOR PRODUCT THEORY FOR MODULES FOR A VERTEX OPERATOR ALGEBRA
- VERTEX OPERATOR ALGEBRAS AND THE VERLINDE CONJECTURE
- RIGIDITY AND MODULARITY OF VERTEX TENSOR CATEGORIES
- Tensor Structures Arising from Affine Lie Algebras. III
- Tensor Structures Arising from Affine Lie Algebras. IV
- JOSEPH IDEALS AND LISSE MINIMAL -ALGEBRAS
- $\boldsymbol{\mathcal{W}}$-algebras with Non-admissible Levels and the Deligne Exceptional Series
- On infinite order simple current extensions of vertex operator algebras
- A quasi-Hopf algebra for the triplet vertex operator algebra
- An Application of Collapsing Levels to the Representation Theory of Affine Vertex Algebras
- Simple current extensions beyond semi-simplicity
- Logarithmic Tensor Category Theory for Generalized Modules for a Conformal Vertex Algebra, I: Introduction and Strongly Graded Algebras and Their Generalized Modules
- Tensor Categories
- On axiomatic approaches to vertex operator algebras and modules
- DIFFERENTIAL EQUATIONS AND INTERTWINING OPERATORS
- FUSION RULES AND COMPLETE REDUCIBILITY OF CERTAIN MODULES FOR AFFINE LIE ALGEBRAS
- Lie superalgebras
- Rationality of admissible affine vertex algebras in the category \(\mathcal O\)
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Tensor categories of affine Lie algebras beyond admissible levels
