On the Structure of Framed Vertex Operator Algebras and Their Pointwise Frame Stabilizers

By C. Lam, H. Yamauchi. 2006

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In this paper, we study the structure of a general framed vertex operator algebra (VOA). We show that the structure codes (C,D) of a framed VOA V satisfy certain duality conditions. As a consequence, we prove that every framed VOA is a simple current extension of the associated binary code VOA VC. This result suggests the feasibility of classifying framed vertex operator algebras, at least if the central charge is small. In addition, the pointwise frame stabilizer of V is studied. We completely determine all automorphisms in the pointwise stabilizer, which are of order 1, 2 or 4. The 4A-twisted sector and the 4A-twisted orbifold theory of the famous moonshine VOA $$V^\natural$$ are also constructed explicitly. We verify that the top module of this twisted sector is of dimension 1 and of weight 3/4 and the VOA obtained by 4A-twisted orbifold construction of $$V^\natural$$ is isomorphic to $$V^\natural$$ itself.

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Unitary vertex operator algebras (2013, background): “ unitary vertex operator algebra. Recall that an irreducible V-module Mis called simple current if the tensor product M⊠M1 is an irreducible V-module for any irreducible V-module M1. It was proved in [LY] that there exists a vertex operator algebra structure on U = V ⊕ M if M is a simple current V-m”