4 research outputs found
Weighted Traces on Algebras of Pseudo-Differential Operators and Geometry of Loop Groups
Using {\it weighted traces} which are linear functionals of the type defined on the whole
algebra of (classical) pseudo-differential operators (P.D.O.s) and where 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.Comment: 36 page
Les clairieres de Saint-Pierre-de-Chartreuse : elements de connaissances pour la gestion patrimoniale de ces structures paysageres
Available from INIST (FR), Document Supply Service, under shelf-number : GR 1762 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc