Freely Generated Vertex Algebras and Non–Linear Lie Conformal Algebras
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- Sole, A. & Kac, V. Commun. Math. Phys. (2005) 254: 659. doi:10.1007/s00220-004-1245-x
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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.