Exponential Baker-campbell-hausdorff Formula and Compressed Kashiwara-vergne Conjecture
نویسنده
چکیده
Abstract. The classical Baker-Campbell-Hausdorff formula gives a recursive way to compute the Hausdorff series H = log(ee ) for non-commuting X, Y . Formally H lives in a completion L̂ of the free Lie algebra L generated by X, Y . We prove that there are F, G ∈ [L̂, L̂] such that H = e Xe + eY e. We describe explicitly all symmetric solutions to the Kashiwara-Vergne conjecture in Lie algebras L, where commutators of commutators vanish, i.e. [
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