ON A CLASS OF CLOSED COCYCLES FOR ALGEBRAS OF NON-FORMAL, POSSIBLY UNBOUNDED, PSEUDODIFFERENTIAL OPERATORS - Archive ouverte HAL Access content directly
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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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Dates and versions

hal-03066255 , version 1 (15-12-2020)

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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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