On the geometry of pseudodifferential operators based on renormalized traces
JP Magnot - arXiv preprint arXiv:2007.00387, 2020 - arxiv.org
In this article, we examine the geometry of a group of Fourier-integral operators, which is the
central extension of $ Diff (S^ 1) $ with a group of classical pseudo-differential operators of …
central extension of $ Diff (S^ 1) $ with a group of classical pseudo-differential operators of …
On Diff (M)-pseudo-differential operators and the geometry of non linear Grassmannians
JP Magnot - Mathematics, 2015 - mdpi.com
We consider two principal bundles of embeddings with total space E mb (M, N), with
structure groups D iff (M) and D iff+(M), where D iff+(M) is the groups of orientation …
structure groups D iff (M) and D iff+(M), where D iff+(M) is the groups of orientation …
On smooth infinite dimensional grassmannians, splittings and non-commutative generalized cross-ratio mappings
JP Magnot - arXiv preprint arXiv:2404.16888, 2024 - arxiv.org
We describe basic diffeological structures related to splittings and Grassmannians for infinite
dimensional vector spaces. We analyze and expand the notion of non-commutative cross …
dimensional vector spaces. We analyze and expand the notion of non-commutative cross …
On a class of closed cocycles for algebras of non-formal, possibly unbounded, pseudodifferential operators
JP Magnot - arXiv preprint arXiv:2012.06941, 2020 - arxiv.org
In this article, we consider algebras $\mathcal {A} $ of non-formal pseudodifferential
operators over $ S^ 1$ which contain $ C^\infty (S^ 1), $ understood as multiplication …
operators over $ S^ 1$ which contain $ C^\infty (S^ 1), $ understood as multiplication …
On algebras and groups of formal series over a small category, non-abelian stochastic cosurfaces and topological quantum field theories
JP Magnot - 2020 - hal.science
Based on the example of stochastic cosurfaces, we develop the notion of groups of series
indexed by a graded small category, with coefficients in a Fr\" olicher algebra. The presence …
indexed by a graded small category, with coefficients in a Fr\" olicher algebra. The presence …
On algebras and groups of formal series over a groupoid and application to some spaces of cobordism
JP Magnot - arXiv preprint arXiv:1507.00932, 2015 - arxiv.org
We develop here a concept of deformed algebras and their related groups through two
examples. Deformed algebras are obtained from a fixed algebra by deformation along a …
examples. Deformed algebras are obtained from a fixed algebra by deformation along a …
From infinitesimal symmetries to deformed symmetries of Lax-type equations
JP Magnot - Journal of Physics: Conference Series, 2015 - iopscience.iop.org
Using the procedure initiated in [14], we deform Lax-type equations though a scaling of the
time parameter. This gives an equivalent (deformed) equation which is integrable in terms of …
time parameter. This gives an equivalent (deformed) equation which is integrable in terms of …
Deformed algebras: examples and application to Lax equations
JP Magnot - arXiv preprint arXiv:1402.5629, 2014 - arxiv.org
We develop here a concept of deformed algebras through three examples and an
application. Deformed algebras are obtained from a fixed algebra by deformation along a …
application. Deformed algebras are obtained from a fixed algebra by deformation along a …