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

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dc.creatorCardona, A.
dc.creatorDucourtioux, C.
dc.creatorMagnot, J. P.
dc.creatorPaycha, S.
dc.date2000-01-21
dc.date.accessioned2026-07-07T04:33:23Z
dc.date.available2026-07-07T04:33:23Z
dc.descriptionUsing {\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.
dc.description36 pages
dc.identifierhttps://arxiv.org/abs/math/0001117
dc.identifierhttp://arxiv.org/abs/math/0001117
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58555
dc.subjectOperator Algebras
dc.subjectMathematical Physics
dc.titleWeighted Traces on Algebras of Pseudo-Differential Operators and Geometry of Loop Groups
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