A Cartan decomposition for finite vertex algebras

Details A Cartan decomposition for finite vertex algebras A Cartan decomposition for finite vertex algebras

2011-12-13

arxiv.org/abs/1112.2969v1

Mathematics

Quantum Algebra

Scientific paper

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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