Geometric vertex operator algebras

Abstract

In this chapter we define the notion of geometric vertex operator algebra and prove that it is equivalent to that of vertex operator algebra. In Section 5.1 we discuss briefly graded vector spaces with finite-dimensional homogeneous subspaces and fix some notations. In Section 5.2 we define the notion of geometric vertex operator algebra assuming the convergence of certain projective factors. (The convergence of these projective factors will be proved in Section 6.7.) In Section 5.3, we give the algebraic definition of vertex operator algebra. We also give some immediate consequences of this definition and the duality properties in this section.