The bosonic vertex operator algebra on a genus g riemann surface m. Keller eth zuric h hs 2017 under construction version as of. Pdf conformal field theory, vertex operator algebras and. Subsequently the foundations underwent some simpli. The online database of vertex operator algebras and modular categories version 0. A vertex operator superalgebra v v0 v1 with v1 0 is called a vertex operator algebra and we call it a voa for short. Complete definitions of the notions of vertex algebra and vertex operator algebra, using commuting formal variables, and are given below. The original vertex operator algebras are equivalent to conformal vertex algebra in modern texts. Similarly, a vertex operator superalgebra is shortly referred to as a super voa or an svoa. Fusion rules for the free bosonic orbifold vertex operator. The duality between vertex operator algebras and coalgebras, modules and comodules keith hubbard abstract. Pdf the bosonic vertex operator algebra on a genus g.
The traditional definition of vertex operator algebra voa is long and tends to be. Vertex operator algebra encyclopedia of mathematics. We construct an equivalence between the categories of vertex operator algebras and vertex operator coalgebras. The online database of vertex operator algebras and. In fact one vertex operator algebra encodes only one chiralholomorphic half of such a genus0 2d cft. Pdf a generalized vertex operator algebra for heisenberg. We then investigate to what degree weak modules, generalized modules and ordinary modules carry corre. From this point of view, the notion of vertex operator thus appeared before the underlying concept of vertex algebra. Conformal field theory, vertex operator algebras and operator algebras. A generalized vertex operator algebra for heisenberg intertwiners m. The definition of vertex algebra with either minimal or maximal axioms is equivalent to borcherds definition in. Pdf introduction to vertex operator algebras imoonshine. Vertex algebras, walgebras, and applications 20142015.
602 314 508 1074 1051 508 240 1552 137 1291 536 262 742 1024 621 747 503 557 958 1457 672 928 1341 239 89 1320 1001 805 1300 822 276 882 399 1493 1400 687 677 1387