Representations of vertex operator superalgebras over an arbitrary field

Abstract

An associative algebra A(V) for a vertex operator superalgebra V over an arbitrary algebraically closed field F with chF≠2 is constructed so that the top level of an admissible V-module is naturally an A(V)-module. The highest weight module theory of V is investigated by using A(V) and a one to one correspondence between irreducible A(V)-modules and irreducible admissible V-modules is obtained. Moreover, A(V) is semisimple if V is rational. An A(V)-bimodule A(M) for any admissible V-module M is also constructed and is used to study the fusion rules among V-modules.