I give a short proof of the following algebraic statement: in a simple vertex algebra, the underlying Lie conformal algebra is either abelian, or it is an irreducible central extension of a simple Lie conformal algebra. This provides many examples of non-finite simple Lie conformal algebras, and should prove useful for classification purposes.

A remark on simplicity of vertex algebras and Lie conformal algebras / D'Andrea, Alessandro. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 319:5(2008), pp. 2106-2112. [10.1016/j.jalgebra.2007.09.009]

A remark on simplicity of vertex algebras and Lie conformal algebras

D'ANDREA, Alessandro
2008

Abstract

I give a short proof of the following algebraic statement: in a simple vertex algebra, the underlying Lie conformal algebra is either abelian, or it is an irreducible central extension of a simple Lie conformal algebra. This provides many examples of non-finite simple Lie conformal algebras, and should prove useful for classification purposes.
2008
lie conformal algebras, simplicity, vertex algebras
01 Pubblicazione su rivista::01a Articolo in rivista
A remark on simplicity of vertex algebras and Lie conformal algebras / D'Andrea, Alessandro. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 319:5(2008), pp. 2106-2112. [10.1016/j.jalgebra.2007.09.009]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/103773
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