arXiv subjects
Publications and source records attributed to Gaywalee Yamskulna.
We continue with [LY] to construct and classify graded simple twisted modules for the $\N$-graded vertex algebras constructed by Gorbounov, Malikov and Schechtman from vertex algebroids. Meanwhile we determine the full automorphism groups of those $\N$-graded vertex algebras in terms of the automorphism groups of the corresponding vertex algebroids.
We study the family of vertex algebras associated with vertex algebroids, constructed by Gorbounov, Malikov, and Schechtman. As the main result, we classify all the (graded) simple modules for such vertex algebras and we show that the equivalence classes of graded simple modules one-to-one correspond to the equivalence classes of simple modules for the Lie algebroids associated with the vertex algebroids. To achieve our goal, we construct and exploit a Lie algebra from a given vertex algebroid.
Let V be a simple vertex operator algebra and let G be a finite automorphism group of V. In [DY], it was shown that any irreducible V-module is a completely reducible V^G-module where V^G is the G-invariant sub-vertex operator algebra of V. In this paper, we give an alternative proof of this fact using the theory of skew group algebras. We also extend this result to any irreducible g-twisted V-module when g is in the center of G and V is a g-rational vertex operator algebra.
Let L be a rank one positive definite even lattice. We prove that a vertex operator algebra (VOA) V_L^+ satisfies the C_2 condition. Here, V_L^+ is a fixed point sub-VOA of the VOA V_L associated with the automorphism lifted from the -1 isometry of L.