Finite-dimensional vertex algebra modules over fixed point commutative subalgebras

Details Finite-dimensional vertex algebra modules over fixed point commutative subalgebras Finite-dimensional vertex algebra modules over fixed point commutative subalgebras

2010-12-05

arxiv.org/abs/1012.0957v1

J. Algebra 337(2011) 323-334

Mathematics

Quantum Algebra

20 pages

Scientific paper

10.1016/j.jalgebra.2011.04.024

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.

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