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ON A CLASS OF CLOSED COCYCLES FOR ALGEBRAS OF NON-FORMAL, POSSIBLY UNBOUNDED, PSEUDODIFFERENTIAL OPERATORS

Abstract : In this article, we consider algebras A of non-formal pseudodifferential operators over S 1 which contain C ∞ (S 1), understood as multiplication operators. We apply a construction of Chern-Weil type forms in order to get 2k−closed cocycles. For k = 1, we obtain a cocycle on the algebra of (maybe non classical) pseudodifferential operators with the same cohomology class as the Schwinger cocycle on the algebra of Classical pseudodifferential operators, previously extended and studied by the author on algebras of the same type. We also prove non-triviality in Hochschild cohomology for k = 2.
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https://hal.archives-ouvertes.fr/hal-03066255
Contributor : Jean-Pierre Magnot Connect in order to contact the contributor
Submitted on : Tuesday, December 15, 2020 - 11:01:53 AM
Last modification on : Wednesday, November 3, 2021 - 9:18:43 AM
Long-term archiving on: : Tuesday, March 16, 2021 - 7:12:11 PM

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  • HAL Id : hal-03066255, version 1

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Jean-Pierre Magnot. ON A CLASS OF CLOSED COCYCLES FOR ALGEBRAS OF NON-FORMAL, POSSIBLY UNBOUNDED, PSEUDODIFFERENTIAL OPERATORS. 2020. ⟨hal-03066255⟩

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