Local Systems of Vertex Operators, Vertex Superalgebras and Modules

1994/06/28 by Haisheng Li, Li, Hai-sheng · 6 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.hep-th/9406185

openalex publication_date 1994/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of ``local system of vertex operators'' for a (super) vector space. We first prove that any local system of vertex operators on a (super) vector space M has a natural vertex (super)algebra structure with M as a module. Then we prove that for a vertex (operator) superalgebra V, giving a V-module M is equivalent to giving a vertex (operator) superalgebra homomorphism from V to some local system of vertex operators on M. As applications, we prove that certain lowest weight modules for some well-known infinite-dimensional Lie algebras or Lie superalgebras have natural vertex operator superalgebra structures. We prove the rationality of vertex operator superalgebras associated to standard modules for an affine algebra. We also give an analogue of the notion of the space of linear homomorphisms from one module to another for a Lie algebra by introducing a notion of ``generalized intertwining operators.'' We prove that G(M¹,M²), the space of generalized intertwining operators from one module M¹ to another module M² for a vertex operator superalgebra V, is a generalized V-module. Furthermore, we prove that for a fixed vertex operator superalgebra V and

Citations

• Symmetric invariant bilinear forms on vertex operator algebras

Cited by

• C_n-cofinite twisted modules for C₂-cofinite vertex operator algebras
• A class of vertex operator algebras generated by Virasoro vectors
• Affine vertex operator superalgebra L_sl(2|1)(k,0) at boundary admissible level
• Structure and representations of the coset vertex operator algebra C( L_\widehatosp(1|2)(2,0), L_\widehatosp(1|2)(1,0)^{⊗ 2})
• Y(z)-injective vertex superalgebras and Hopf actions
• Chiral vector bundles

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