泛包络代数的稳定平坦完备化
Stably flat completions of universal enveloping algebras
摘要：
我们研究了局部化（在J.L. Taylor）的复李代数g的泛包络代数U（g）。具体地说，设f：U（g）--> H是某个行为良好的拓扑霍普夫代数H的同态.我们在对偶代数H '上建立了一些条件，这些条件足以使H在U（g）上稳定平坦（即，f是局部化的）。作为应用，我们证明了U（g）的Arens-Michael包络在U（g）上是稳定平坦的，只要g允许正分次.我们还证明了对于每个幂零李代数g，U（g）的Goodman加权完备在U（g）上是稳定平坦的;对于任意g，Rashevskii超完备代数在U（g）上是稳定平坦的.最后，证明了当g可解时，相应的单连通复李群G上解析泛函的Litvinov代数A（G）在U（g）上是稳定平坦的.
英文摘要：
We study localizations (in the sense of J. L. Taylor) of the universal enveloping algebra, U(g), of a complex Lie algebra g. Specifically, let f : U(g) --> H be a homomorphism to some well-behaved topological Hopf algebra H. We formulate some conditions on the dual algebra, H', that are sufficient for H to be stably flat over U(g) (i.e., for f to be a localization). As an application, we prove that the Arens-Michael envelope of U(g) is stably flat over U(g) provided g admits a positive grading. We also show that Goodman's weighted completions of U(g) are stably flat over U(g) for each nilpotent Lie algebra g, and that Rashevskii's hyperenveloping algebra is stably flat over U(g) for arbitrary g. Finally, Litvinov's algebra A(G) of analytic functionals on the corresponding connected, simply connected complex Lie group G is shown to be stably flat over U(g) precisely when g is solvable.
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