Factorization of Formal Exponentials and Uniformization

@article{Barron2000FactorizationOF,
  title={Factorization of Formal Exponentials and Uniformization},
  author={Katrina Deane Barron and Yi-Zhi Huang and James Lepowsky},
  journal={Journal of Algebra},
  year={2000},
  volume={228},
  pages={551-579}
}
Let g be a Lie algebra over a field of characteristic zero equipped with a vector space decomposition g = g − ⊕ g + , and let s and t be commuting formal variables commuting with g. We prove that the map C: sg − [[s, t]] × tg + [[s, t]] → sg − [[s, t]] ⊕ tg + [[s, t]] defined by the Campbell–Baker–Hausdorff formula and given by esg − etg + = eC(sg − , tg + ) for g ± ∈ g ± [[s, t]] is a bijection, as is well known when g is finite-dimensional over R or C, by geometry. It follows that there exist… 
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