4 research outputs found

    Weighted Traces on Algebras of Pseudo-Differential Operators and Geometry of Loop Groups

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    Using {\it weighted traces} which are linear functionals of the type A→trQ(A):=(tr(AQ−z)−z−1tr(AQ−z))z=0A\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 QQ 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

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    Available from INIST (FR), Document Supply Service, under shelf-number : GR 1762 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueSIGLEFRFranc

    Stein spaces

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