On abelian generalized vertex algebras

dc.creatorLi, Haisheng
dc.date2000-08-08
dc.date2000-10-16
dc.date.accessioned2026-07-07T04:36:41Z
dc.date.available2026-07-07T04:36:41Z
dc.descriptionThis 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 $Ω_{V}$ (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 $Ω_{W}$ of a $V$-module $W$ is a natural $Ω_{V}$-module. The automorphism group $\Aut_{Ω_{V}}Ω_{V}$ of the adjoint $Ω_{V}$-module is studied and it is proved to be a central extension of a certain torsion free abelian group by $\C^{\times}$. For certain subgroups $A$ of $\Aut_{Ω_{V}}Ω_{V}$, certain quotient algebras $Ω_{V}^{A}$ of $Ω_{V}$ are constructed. Furthermore, certain functors among the category of $V$-modules, the category of $Ω_{V}$-modules and the category of $Ω_{V}^{A}$-modules are constructed and irreducible $Ω_{V}$-modules and $Ω_{V}^{A}$-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 $Ω_{V}^{A}$-modules is semisimple.
dc.descriptionMinor changes, the final version to appear in Communications in Contemporary Mathematics
dc.identifierhttps://arxiv.org/abs/math/0008062
dc.identifierhttp://arxiv.org/abs/math/0008062
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59692
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.titleOn abelian generalized vertex algebras
dc.typetext

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