Twisted regular representations for vertex operator algebras

This paper is to study what we call twisted regular representations for vertex operator algebras. Let V be a algebra, let σ1,σ2 commuting finite-order automorphisms of and σ=(σ1σ2)−1. Among the main results, any σ-twisted V-module W nonzero complex number z, construct weak σ1⊗σ2-twisted V⊗V-module Dσ1,σ2(z)(W) inside W⁎. W1,W2 σ1-twisted, σ2-twisted V-modules, respectively. We show that P(z)-intertwining maps from W1⊗W2 W⁎ are same as homomorphisms V⊗V-modules into Dσ1,σ2(z)(W). also map equivalent an intertwining type (W′W1W2), which version result Huang Lepowsky. Finally, each τ-twisted M with τ automorphism V, coefficients q-graded trace function lie in Dτ,τ−1(−1)(V) generate τ⊗τ−1-twisted V⊗V-submodule isomorphic M⊗M′.