On intertwining operators and finite automorphism groups of vertex operator algebras

Abstract

Let V be a simple vertex operator algebra and G a finite automorphism group. We give a construction of intertwining operators for irreducible V G -modules which occur as submodules of irreducible V -modules by using intertwining operators for V .We also determine some fusion rules for a vertex operator algebra as an application.

Hopf actions on vertex operator algebras

“…✷ Remark 4.3. In the case H is a group algebra of a finite group, above Proposition was obtained previously in [27]. In fact, the inequality becomes equality in [15] in this case with the help of the quantum dimension identity [8].…”

Fixed point subalgebras of lattice vertex operator algebras by an automorphism of order three

“…The first three fusion rules can be found in [35,Theorem 4] and we can show the last two formulas by applying the same method used there. We shall sketch the proof.…”

The fixed point subalgebra of a lattice vertex operator algebra by an automorphism of order three

“…-25) for i = 1, 2 and ε = 0, 1, 2. In fact, the first four fusion rules, that is, the fusion rules among simple M(0)-modules appearing in untwisted simple V L -modules, can be found in [Tanabe 2005]. The last two fusion rules involve simple M(0)-modules that appear in τ i -twisted simple V L -modules.…”

“…192-193], we can calculate that the dimension of is at most one and it is equal to one if and only if the pair (N 2 , N 3 ) is one of (M T (τ i )(ε), W T (τ i )(ε)), (W T (τ i )(ε), M T (τ i )(ε)), (W T (τ i )(ε), W T (τ i )(ε)) for i = 1, 2, ε = 0, 1, 2. Note that W (0) was denoted by W 0(0) k in [Tanabe 2005]. Now, the desired fusion rules are obtained by [Li 1999a, Proposition 2.10 and Corollary 2.13].…”