2000/08/08 by Haisheng Li, Li, Haisheng
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) #hep-th #math.QA
paper · pdf · doi:10.48550/arxiv.math/0008062
Minor changes, the final version to appear in Communications in Contemporary Mathematics
openalex publication_date 2000/08/08 · arxiv created 2000/10/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the algebraic aspect of a general abelian coset theory with a work of Dong and Lepowsky as our main motivation. It is proved that the vacuum space ΩV (or the space of highest weight vectors) of a Heisenberg algebra in a general vertex operator algebra V has a natural generalized vertex algebra structure in the sense of Dong and Lepowsky and that the vacuum space ΩW of a V-module W is a natural ΩV-module. The automorphism group \Aut_ΩVΩV of the adjoint ΩV-module is studied and it is proved to be a central extension of a certain torsion free abelian group by \C×. For certain subgroups A of \Aut_ΩVΩV, certain quotient algebras ΩVA of ΩV are constructed. Furthermore, certain functors among the category of V-modules, the category of ΩV-modules and the category of ΩVA-modules are constructed and irreducible ΩV-modules and ΩVA-modules are classified in terms of irreducible V-modules. If the category of V-modules is semisimple, then it is proved that the category of ΩVA-modules is semisimple.