Module categories of simple current extensions of vertex operator algebras

In this article, we study module categries of simple current extensions of vertex operator algebras. Under certain assumptions, we show that every module for a rational vertex operator algebra be lifted to a twisted module for an extended algebra with an abelian symmetry.Comment: latex 14 pages, version 2: English corrected, version 3: Hypotheis I is proved in Lemma 3.

2A-orbifold construction and the baby-monster vertex operator superalgebra

In this article we prove that the full automorphism group of the baby-monster vertex operator superalgebra constructed by Hoehn is isomorphic to 2xB, where B is the baby-monster sporadic finite simple group and determine irreducible modules for the baby-monster vertex operator algebra. Our result has many corollaries. In particular, we can prove that the Z_2-orbifold construction with respect to a 2A-involution of the Monster applied to the moonshine vertex operator algebra yields the moonshine vertex operator algebra itself again.Comment: v2: Knowing Tuite's work on 2A-orbifold construction of the moonshine vertex operator algebra, we made a remark on it and revised reference

Vertex operator algebra with two Miyamoto involutions generating S3S_3

In this article we study a VOA with two Miyamoto involutions generating $S_3$. In \cite{M3}, Miyamoto showed that a VOA generated by two conformal vectors whose Miyamoto involutions generate an automorphism group isomorphic to $S_3$ is isomorphic to one of the four candidates he listed. We construct one of them and prove that our VOA is actually the same as $\mathrm{VA}(e,f)$ studied by Miyamoto. We also show that there is an embedding into the moonshine VOA. Using our VOA, we can define the 3A-triality in the Monster.Comment: latex 26pages, new sections on simple current extensions and embedding into the moonshine VOA are adde