%0 Journal Article
%T Finite-dimensional modules for the polynomial ring in one variable as a vertex algebra
%A Kenichiro Tanabe
%J Mathematics
%D 2007
%I arXiv
%R 10.1016/j.jalgebra.2008.04.023
%X A commutative associative algebra $A$ over ${\mathbb C}$ with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for $A$ as a vertex algebra and the modules for $A$ as an associative algebra are not well understood. In this paper, I give the classification of finite-dimensional indecomposable untwisted or twisted modules for the polynomial ring in one variable over ${\mathbb C}$ as a vertex algebra.
%U http://arxiv.org/abs/0709.0188v1