From: Maarten Bergvelt Subject: Re: vertex algebras and vertex operator algebras Date: 26 Apr 2000 14:24:38 -0500 Newsgroups: sci.math.research Summary: [missing] David Feldman asked: ------------------- What relationship exists between vertex algebras in the sense of Borcherds and vertex operator algebras in the sense of Frenkel, Lepowsky and Meurman's book Vertex Operator Algebras and the Monster? ------------------- The main difference is that in a vertex algebra there need not exist a Virasoro element, i.e., an element f such that the corresponding vertex operator Y(f,z) has components that generate a Virasoro algebra. In a vertex operator algebra the existence of such f is required. Frenkel Lepowsky and Meurman also impose some conditions on a VOA about the underlying vectorspace (should be graded in a specific way) but that is minor. A very good introduction is Kac's Vertex algebras for beginners (get the latest edition, there are some minor errors in the earlier versions). There are also introductions by Borcherds at http://front.math.ucdavis.edu/q-alg/9709033 and http://front.math.ucdavis.edu/q-alg/9706008. A quick search of Math Review (http://ams.rice.edu/mathscinet/search) gives 78 papers containg vertex algebra and 215 containing vertex operator algebra.