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arXiv · 1112.2969

A root space decomposition for finite vertex algebras

Alessandro D'Andrea·Giuseppe Marchei
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Abstract

Let L be a Lie pseudoalgebra, a in L. We show that, if a generates a (finite) solvable subalgebra S= , then one may find a lifting a' in S of [a] in S/S' such that is nilpotent. We then apply this result towards vertex algebras: we show that every finite vertex algebra V admits a decomposition into a semi-direct product V = U + N, where U is a subalgebra of V whose underlying Lie conformal algebra U^lie is a nilpotent self-normalizing subalgebra of V^lie, and N is a canonically determined ideal contained in the nilradical Nil V.

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BibTeXRIS

Alessandro D'Andrea, Giuseppe Marchei. 2012-10-18. A root space decomposition for finite vertex algebras. https://arxiv.org/abs/1112.2969

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