Communications in Mathematical Physics

, Volume 254, Issue 3, pp 659–694 | Cite as

Freely Generated Vertex Algebras and Non–Linear Lie Conformal Algebras

  • Alberto De SoleEmail author
  • Victor G. Kac


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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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© 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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