Nonlocal vertex algebras generated by formal vertex operators

Details Nonlocal vertex algebras generated by formal vertex operators Nonlocal vertex algebras generated by formal vertex operators

2005-02-11

arxiv.org/abs/math/0502244v2

Mathematics

Quantum Algebra

50 pages; Dedicated to James Lepowsky and Robert Wilson, New title and a lot of changes in exposition and organization

Scientific paper

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 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.

Affiliated with

Also associated with

No associations

Rating

Nonlocal vertex algebras generated by formal vertex operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nonlocal vertex algebras generated by formal vertex operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonlocal vertex algebras generated by formal vertex operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-54964