ON THE GEOMETRY OF Dif f (S 1 )−PSEUDODIFFERENTIAL OPERATORS BASED ON RENORMALIZED TRACES - Archive ouverte HAL Access content directly
Journal Articles Proceedings of the International Geometry Center Year : 2021

ON THE GEOMETRY OF Dif f (S 1 )−PSEUDODIFFERENTIAL OPERATORS BASED ON RENORMALIZED TRACES

Abstract

In this article, we examine the geometry of a group of Fourier-integral operators, which is the central extension of Dif f (S 1) with a group of classical pseudo-differential operators of any order. Several subgroups are considered , and the corresponding groups with formal pseudodifferential operators are defined. We investigate the relationship of this group with the restricted general linear group GLres, we define a right-invariant pseudo-Riemannian metric on it that extends the Hilbert-Schmidt Riemannian metric by the use of renormalized traces of pseudo-differential operators, and we describe classes of remarkable connections. MSC (2010) : 22E66, 47G30, 58B20, 58J40
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Dates and versions

hal-02887578 , version 1 (02-07-2020)

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Jean-Pierre Magnot. ON THE GEOMETRY OF Dif f (S 1 )−PSEUDODIFFERENTIAL OPERATORS BASED ON RENORMALIZED TRACES. Proceedings of the International Geometry Center, 2021, 14 (1), pp.19-47. ⟨10.15673/tmgc.v14i1.1784⟩. ⟨hal-02887578⟩
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