Freely generated vertex algebras and non-linear Lie conformal algebras

Details Freely generated vertex algebras and non-linear Lie conformal algebras Freely generated vertex algebras and non-linear Lie conformal algebras

2003-12-15

arxiv.org/abs/math-ph/0312042v3

Physics

Mathematical Physics

38 pages

Scientific paper

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.

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