Finite-dimensional modules for the polynomial ring in one variable as a vertex algebra

Details Finite-dimensional modules for the polynomial ring in one variable as a vertex algebra Finite-dimensional modules for the polynomial ring in one variable as a vertex algebra

2007-09-03

arxiv.org/abs/0709.0188v1

J. Algebra 320(2008) 1261-1274

Mathematics

Quantum Algebra

17 pages

Scientific paper

10.1016/j.jalgebra.2008.04.023

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.

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