伪微分算子代数上的加权迹与环群几何
Weighted Traces on Algebras of Pseudo-Differential Operators and Geometry of Loop Groups
摘要：
利用定义在（经典）伪微分算子（P.D.O.s）全代数上的$$A\to tr^Q(A):=(tr(A Q^{-z})-z^{-1} tr(A Q^{-z}))_{z=0}$$型线性泛函{ \it加权迹}，其中$Q$是某个正可逆椭圆算子，我们根据伪微分算子的上同调研究了环群的几何.我们建立了一个几何框架来研究一类无穷维流形，在这个几何框架中，我们重新利用加权迹恢复了关于圈群几何的一些结果。一路上，我们调查性质的扩展的Radul和Schwinger上循环定义的帮助下，加权迹。
英文摘要：
Using {\it weighted traces} which are linear functionals of the type $$A\to tr^Q(A):=(tr(A Q^{-z})-z^{-1} tr(A Q^{-z}))_{z=0}$$ defined on the whole algebra of (classical) pseudo-differential operators (P.D.O.s) and where $Q$ is some positive invertible elliptic operator, we investigate the geometry of loop groups in the light of the cohomology of pseudo-differential operators. We set up a geometric framework to study a class of infinite dimensional manifolds in which we recover some results on the geometry of loop groups, using again weighted traces. Along the way, we investigate properties of extensions of the Radul and Schwinger cocycles defined with the help of weighted traces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
