Nonlocal vertex algebras generated by formal vertex operators |
| |
Authors: | Haisheng Li |
| |
Institution: | (1) Department of Mathematical Sciences, Rutgers University, Camden, NJ, 08102, U.S.A;(2) Department of Mathematics, Harbin Normal University, Harbin, China |
| |
Abstract: | This 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 foundations 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. |
| |
Keywords: | 17B69 |
本文献已被 SpringerLink 等数据库收录! |
|