论文标题
面包板 - 贝克 - 霍斯多夫定理的相对较短的独立证明
A relatively short self-contained proof of the Baker-Campbell-Hausdorff theorem
论文作者
论文摘要
我们给出了Baker-campbell-Hausdorff定理的新的纯代数证明，该证明指出$ \ log（e^ae^b）$的正式扩展的均匀组成部分是多项式。我们的证明是基于这些组件的复发公式和一个引理，该公式指出，如果在某些条件下，一个非公认变量的换向器和给定的多项式是一个谎言多项式，那么给定的多项式本身就是谎言。
We give a new purely algebraic proof of the Baker-Campbell-Hausdorff theorem, which states that the homogeneous components of the formal expansion of $\log(e^Ae^B)$ are Lie polynomials. Our proof is based on a recurrence formula for these components and a lemma that states that if under certain conditions a commutator of a non-commuting variable and a given polynomial is a Lie polynomial, then the given polynomial itself is a Lie polynomial.
