Communications in Mathematical Physics

, Volume 254, Issue 3, pp 659–694

Freely Generated Vertex Algebras and Non–Linear Lie Conformal Algebras


DOI: 10.1007/s00220-004-1245-x

Cite this article as:
Sole, A. & Kac, V. Commun. Math. Phys. (2005) 254: 659. doi:10.1007/s00220-004-1245-x


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Department of MathematicsMIT 77 Massachusetts AvCambridgeUSA

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