Finite-dimensional vertex algebra modules over fixed point commutative subalgebras

Abstract

Let $A$ be a connected commutative $\C$-algebra with derivation $D$, $G$ a finite linear automorphism group of $A$ which preserves $D$, and $R=A^G$ the fixed point subalgebra of $A$ under the action of $G$. We show that if $A$ is generated by a single element as an $R$-algebra and is a Galois extension over $R$ in the sense of M. Auslander and O. Goldman, then every finite-dimensional vertex algebra $R$-module has a structure of twisted vertex algebra $A$-module.

20 pages

References in corpus (5)

• Representations of vertex operator algebra V_L^+ for rank one lattice L
• Z_3 symmetry and W_3 algebra in lattice vertex operator algebras
• Classification of irreducible modules for the vertex operator algebra M(1)^+, II: higher rank
• Finite-dimensional modules for the polynomial ring in one variable as a vertex algebra
• Finite-dimensional vertex algebra modules over fixed point differential subfields