A Root Space Decomposition for Finite Vertex Algebras
نویسندگان
چکیده
Let L be a Lie pseudoalgebra, a ∈ L. We show that, if a generates a (finite) solvable subalgebra S = 〈a〉 ⊂ L, then one may find a lifting ā ∈ S of [a] ∈ S/S such that 〈ā〉 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 is a nilpotent self-normalizing subalgebra of V , and N = V [∞] is a canonically determined ideal contained in the nilradical NilV . 2010 Mathematics Subject Classification: 17B69
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