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 unique, up to isomorphism, 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. © Springer-Verlag 2005.
CITATION STYLE
De Sole, A., & Kac, V. G. (2005). Freely generated vertex algebras and non-linear Lie conformal algebras. Communications in Mathematical Physics, 254(3), 659–694. https://doi.org/10.1007/s00220-004-1245-x
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