Abstract

For any vertex operator algebra V, finite automorphism g of V of order T and m,n∈(1/T)Z+, we construct a family of associative algebras Ag,n(V) and Ag,n(V)−Ag,m(V)-bimodules Ag,n,m(V) from the point of view of representation theory. We prove that the algebra Ag,n(V) is identical to the algebra Ag,n(V) constructed by Dong, Li and Mason, and that the bimodule Ag,n,m(V) is identical to Ag,n,m(V) which was constructed by Dong and Jiang. We also prove that the Ag,n(V)−Ag,m(V)-bimodule Ag,n,m(V) is isomorphic to U(V[g])n−m/U(V[g])n−m−m−1/T, where U(V[g])k is the subspace of degree k of the (1/T)Z-graded universal enveloping algebra U(V[g]) of V with respect to g and U(V[g])kl is some subspace of U(V[g])k. And we show that all these bimodules Ag,n,m(V) can be defined in a simpler way.

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