2004/04/05 by Haisheng Li, Li, Haisheng
Mathematics · Physics and Astronomy · #17B67 #17B69 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:17B67 #msc:17B69
paper · pdf · doi:10.48550/arxiv.math/0404110
62 pages
arxiv created 2004/04/05 · openalex publication_date 2004/04/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, a new construction of vertex algebras from more general vertex operators is given and a notion of quasi module for vertex algebras is introduced and studied. More specifically, a notion of quasi local subset(space) of \Hom (W,W((x))) for any vector space W is introduced and studied, generalizing the notion of usual locality in the most possible way, and it is proved that on any maximal quasi local subspace there exists a natural vertex algebra structure and that any quasi local subset of \Hom (W,W((x))) generates a vertex algebra. Furthermore, a notion of quasi module for a vertex algebra is introduced and it is proved that W is a quasi module for each of the vertex algebras generated by quasi local subsets of \Hom (W,W((x))). A notion of Γ-vertex algebra is also introduced and studied, where Γ is a subgroup of the multiplicative group \C× of nonzero complex numbers. It is proved that any maximal quasi local subspace of \Hom (W,W((x))) is naturally a Γ-vertex algebra and that any quasi local subset of \Hom (W,W((x))) generates a Γ-vertex algebra. It is also proved that a Γ-vertex algebra exactly amounts to a vertex algebra equipped with a Γ-module structure which satisfies a certain compatibility condition. Finally, three families of examples are given, involving twisted affine Lie algebras, certain quantum Heisenberg algebras and certain quantum torus Lie algebras.