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Exponential Baker-Campbell-Hausdorff formula and applications to formal vector fields | V. Kurlin
; | Date: |
14 Jun 2006 | Subject: | Quantum Algebra; Algebraic Topology | Abstract: | The classical Baker-Campbell-Hausdorff formula gives a recursive way to compute the Hausdorff series $H=log(e^Xe^Y)$ for non-commuting $X,Y$. Formally $H$ lives in a completion $hat L$ of the free Lie algebra $L$ generated by $X,Y$. We prove that there are $F,Gin[hat L,hat L]$ such that $H=e^F X e^{-F}+e^G Y e^{-G}$. We give a closed expression for $H$ in the Lie algebra of formal vector fields on the line. | Source: | arXiv, math/0606330 | Services: | Forum | Review | PDF | Favorites |
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