Abstract
For infinite dimensional Lie algebras G, the theory of formal deformations does not generally give decisive results about analytic deformations. In particular, if Gt is a family of Lie algebras depending holomorphically on t with G 0=G, and if (Gt) is formally equivalent to G[[t]], it does not necessarily follow that Gt is isomorphic toG for small ∣t∣. However, one may ask if Ĝt is isomorphic to Ĝ for small ∣t∣,Ĝ t and Ĝ being suitable completions of Gt and G respectively. In this Letter, this question is discussed when G=W, the Witt algebra.
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Guerrini, L. Formal and Analytic Deformations of the Witt Algebra. Letters in Mathematical Physics 46, 121–129 (1998). https://doi.org/10.1023/A:1007521413901
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DOI: https://doi.org/10.1023/A:1007521413901