Wheeling：Duflo同构的一个图解模拟
Wheeling: A diagrammatic analogue of the Duflo isomorphism
摘要：
构造并证明了李代数的对称代数的不变子代数与泛包络代数的中心之间的Duflo同构的一个图解形式。这个版本意味着原来的度量化李代数（李代数与不变的非退化双线性型）。作为这个同构的一个应用，我们将计算所有阶的unknot和Hopf链的Kontsevich积分。在证明的核心，我们使用了一个基本性质的霍普夫链，可以概括为方程"1+1= 2“在算盘算术：加倍一个组成部分的霍普夫链相当于采取两个连接的和霍普夫链。当适当地解释时，霍普夫链的这一性质恰好是Duflo映射为乘法所需的性质。为了计算解结的Kontsevich积分，我们使用解结的一个性质，可以用"n * 0 = 0“来概括：解结的n重连接电缆也是解结。
英文摘要：
We construct and prove a diagrammatic version of the Duflo isomorphism between the invariant subalgebra of the symmetric algebra of a Lie algebra and the center of the universal enveloping algebra. This version implies the original for metrized Lie algebras (Lie algebras with an invariant non-degenerate bilinear form). As an application of this isomorphism, we will compute the Kontsevich integral of the unknot and the Hopf link to all orders. At the core of the proof, we use an elementary property of the Hopf link which can be summarized by the equation ``1+1=2'' in abacus arithmetic: doubling one component of the Hopf link is equivalent to taking the connected sum of two Hopf links. This property of the Hopf link turns out, when suitably interpreted, to be exactly the property required for the Duflo map to be multiplicative. To compute the Kontsevich integral of the unknot, we use a property of the unknot that can be summarized by ``n * 0 = 0'': the n-fold connected cabling of the unknot is again an unknot.
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