Nonlocal vertex algebras generated by formal vertex operators

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dc.creatorLi, Haisheng
dc.date2005-02-11
dc.date2005-06-01
dc.date.accessioned2026-07-07T05:16:54Z
dc.date.available2026-07-07T05:16:54Z
dc.descriptionThis is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay the foundation for this study. For any vector space $W$, we study what we call quasi compatible subsets of $\Hom (W,W((x)))$ and we prove that any maximal quasi compatible subspace has a natural nonlocal (namely noncommutative) vertex algebra structure with $W$ as a natural faithful quasi module in a certain sense and that any quasi compatible subset generates a nonlocal vertex algebra with $W$ as a quasi module. In particular, taking $W$ to be a highest weight module for a quantum affine algebra we obtain a nonlocal vertex algebra with $W$ as a quasi module. We also formulate and study a notion of quantum vertex algebra and we give general constructions of nonlocal vertex algebras, quantum vertex algebras and their modules.
dc.description50 pages; Dedicated to James Lepowsky and Robert Wilson, New title and a lot of changes in exposition and organization
dc.identifierhttps://arxiv.org/abs/math/0502244
dc.identifierhttp://arxiv.org/abs/math/0502244
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74162
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subject17B69
dc.titleNonlocal vertex algebras generated by formal vertex operators
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