math.QA/9903038 [abs, src, ps, other] : Title: Quantum vertex algebras Authors: Richard E. Borcherds Comments: 18 pages, plain tex Subj-class: Quantum Algebra; Category Theory concludes with a large set of problems some of which are strictly n-categorical The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to construct many examples of vertex algebras, in particular by using an analogue of the construction of a twisted group ring from a bicharacter of a group. We also define quantum vertex algebras as singular braided rings in the same category and construct some examples of them. The constructions work just as well for higher dimensional analogues of vertex algebras. (18kb) ************************************************************ Jim Stasheff jds@math.upenn.edu 146 Woodland Dr Lansdale PA 19446 (215)822-6707 Jim Stasheff jds@math.unc.edu Math-UNC (919)-962-9607 Chapel Hill NC FAX:(919)-962-2568 27599-3250