Freely generated vertex algebras and non-linear Lie conformal algebras
Mathematical Physics
2015-12-18 v3 math.MP
Exactly Solvable and Integrable Systems
Abstract
We introduce the notion of a non--linear Lie conformal superalgebra and prove a PBW theorem for its universal enveloping vertex algebra. We also show that conversely any graded freely generated vertex algebra is the universal enveloping algebra of a non--linear Lie conformal superalgebra. This correspondence will be applied in the subsequent work to the problem of classification of finitely generated simple graded vertex algebras.
Cite
@article{arxiv.math-ph/0312042,
title = {Freely generated vertex algebras and non-linear Lie conformal algebras},
author = {Alberto De Sole and Victor Kac},
journal= {arXiv preprint arXiv:math-ph/0312042},
year = {2015}
}
Comments
38 pages