Local systems of vertex operators, vertex superalgebras and modules

1996/06/01 by Hai-Sheng Li · 466 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Affine Lie algebra #Algebra over a field #Algebraic structures and combinatorial models #Current algebra #Discrete mathematics #Graph #Homomorphism #Jordan algebra #Lie superalgebra #Mathematics #Nonlinear Waves and Solitons #Operator (biology) #Operator algebra #Pure mathematics #Superalgebra #Vertex (graph theory) #Vertex operator algebra

paper · doi:10.1016/0022-4049(95)00079-8

published in Journal of Pure and Applied Algebra 109(2), 143-195 (Elsevier BV)

openalex publication_date 1996/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Cited by

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• A construction of some ideals in affine vertex algebras
• On axiomatic aspects of N=2 vertex superalgebras with odd formal variables, and deformations of N=1 vertex superalgebras
• Some finite properties for vertex operator superalgebras
• Quantum vertex C((t))-algebras and quantum affine algebras
• Representation theory and tensor product theory for vertex operator algebras
• On replacement axioms for the Jacobi identity for vertex algebras and their modules
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• Modular Virasoro Vertex Algebras and Affine Vertex Algebras
• C_n-cofinite twisted modules for C₂-cofinite vertex operator algebras
• Mirror Extensions of Vertex Operator Algebras
• Quantum vertex algebras and their phi-coordinated quasi modules
• Ordered spanning sets for quasimodules for Mobius vertex algebras
• Toroidal extended affine Lie algebras and vertex algebras
• (G,χ_ϕ)-equivariant ϕ-coordinated modules for vertex algebras
• Embedding of certain vertex algebras without vacuum into vertex algebras
• On quasi modules at infinity for vertex algebras
• Automorphism groups and derivation algebras of finitely generated vertex operator algebras
• On certain higher dimensional analogues of vertex algebras
• Toroidal vertex algebras and their modules
• Vertex operator algebras associated to the Virasoro algebra over an arbitrary field
• Modules for a sheaf of Lie algebras on loop manifolds
• A class of vertex operator algebras generated by Virasoro vectors
• Generalized vertex algebras generated by parafermion-like vertex operators
• A new construction of vertex algebras and quasi modules for vertex algebras
• Affine vertex operator superalgebra L_sl(2|1)(k,0) at boundary admissible level
• Classification of irreducible modules of certain subalgebras of free boson vertex algebra
• A Z₂-orbifold model of the symplectic fermionic vertex operator superalgebra
• Holomorphic Vertex Operator Algebras of Small Central Charges
• Simple vertex operator algebras are nondegenerate
• Hom functor and the associativity of tensor products of modules for vertex operator algebras
• Structure and representations of the coset vertex operator algebra C( L_\widehatosp(1|2)(2,0), L_\widehatosp(1|2)(1,0)^{⊗ 2})
• ϕ_ε-coordinated modules for vertex algebras
• The global sections of the chiral de Rham complex on a Kummer surface
• Y(z)-injective vertex superalgebras and Hopf actions
• Quasi-modular forms and trace functions associated to free boson and lattice vertex operator algebras
• Rational Vertex Operator Algebras and the Effective Central Charge
• Vertex algebras associated with elliptic affine Lie algebras
• On twisted representations of vertex algebras
• Nonlocal vertex algebras generated by formal vertex operators
• Quantum Dimensions and Quantum Galois Theory
• Introduction to vertex operator algebras I
• Extended affine Lie algebras, vertex algebras, and reductive groups
• On certain vertex algebras and their modules associated with vertex algebroids
• N=1 Neveu-Schwarz vertex operator superalgebras over Grassmann algebras and with odd formal variables
• Quantum vertex F((t))-algebras and their modules
• The Z₂ Orbifold of the Universal Affine Vertex Algebra
• On rationality of vertex operator superalgebras
• The radical of a vertex operator algebra associated to a module
• On Z-graded associative algebras and their N-graded modules
• Level-Rank Duality for Vertex Operator Algebras of types B and D
• A recurrence relation for characters of highest weight integrable modules for affine Lie algebras
• Representations of the fixed point subalgebra of the vertex algebra associated to a non-degenerate even lattice by an automorphism of order 2
• Presentations of the principal subspaces of the higher-level standard \widehat\mathfraksl(3)-modules
• Representations of Lie algebra of vector fields on a torus and chiral de Rham complex
• Certain associative algebras similar to U(sl₂) and Zhu's algebra A(V_L)
• Leading terms of relations for standard modules of affine Lie algebras C_n\sp(1)
• Quasi-particle bases of principal subspaces for the affine Lie algebras of types B_l⁽¹⁾ and C_l⁽¹⁾
• Vertex Algebras and Commutative Algebras
• Associating quantum vertex algebras to Lie algebra \gl_∞
• Associating quantum vertex algebras to certain deformed Heisenberg Lie algebras
• Extension of vertex operator algebra V_H₄(ℓ,0)
• Regularity of certain vertex operator algebras with two generators
• (d,σ)-twisted Affine-Virasoro superalgebras
• Representations of the parafermion vertex operator algebras
• On the unitary structures of vertex operator superalgebras
• Rationality of unitary N=2 vertex operator superalgebras
• Combinatorics of free vertex algebras
• Representations of N=2 superconformal vertex algebra
• Simple smooth modules over the Lie algebras of polynomial vector fields
• Vertex algebras and vertex Poisson algebras
• Regular representations of vertex operator algebras, I
• Vertex operator algebras and the zeta function
• On certain categories of modules for affine Lie algebras
• Introduction to vertex operator algebras II
• On a symmetry of the category of integrable modules
• A realization of certain modules for the N=4 superconformal algebra and the affine Lie algebra A₂ ⁽¹⁾
• An analogue of the Hom functor and a generalized nuclear democracy theorem
• 2A-orbifold construction and the baby-monster vertex operator superalgebra
• Some quantum vertex algebras of Zamolodchikov-Faddeev type
• Representations of toroidal extended affine Lie algebras
• Intertwining operators and modular invariance
• Twisted modules for quantum vertex algebras
• Nonassociative algebras of anti-biderivation-type
• The rank two lattice type vertex operator algebras V_L⁺ and their automorphism groups
• Vertex operator algebras associated to admissible representations of sl₂
• K-theory associated to vertex operator algebras
• Intertwining operator algebras and vertex tensor categories for affine Lie algebras
• CONSTRUCTING QUANTUM VERTEX ALGEBRAS
• Deformation of central charges, vertex operator algebras whose Griess algebras are Jordan algebras
• Compact automorphism groups of vertex operator algebras
• Finite vertex algebras and nilpotence
• Vertex Algebras, Lie Algebras and Superstrings
• Certain Extensions¶of Vertex Operator Algebras of Affine Type
• ℏ -adic Quantum Vertex Algebras and Their Modules
• Representations of certain non-rational vertex operator algebras of affine type
• Heisenberg VOAs over Fields of Prime Characteristic and Their Representations
• The Vertex Algebra M(1) + and Certain Affine Vertex Algebras of Level -1
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• Invariant bilinear forms on a vertex algebra and the radical
• Regular representations and Huang-Lepowsky's tensor functors for vertex operator algebras
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• Representations of the Orbifold VOAS L_\widehat\mathfrak sl₂(k,0)^K and the Commutant VOAS C_L_\widehat\mathfrak so_m(1,0)^{⊗ 3}(L_\widehat\mathfrak so_m(3,0))
• Twisted Logarithmic Modules of Vertex Algebras
• The Structure of the Kac–Wang–Yan Algebra
• A Hilbert theorem for vertex algebras
• A Commutant Realization of 𝒲n(2) at Critical Level
• Modularity in Orbifold Theory for Vertex Operator Superalgebras
• Super Quantum Airy Structures. [europepmc]